%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE179+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:30 PM UTC 2026
% Result : Satisfiable 0.13s 0.64s
% Output : Saturation 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] : multiplication(A,omega(A)) = omega(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( leq(A,addition(multiplication(B,A),C))
=> leq(A,addition(omega(B),multiplication(star(B),C))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( ! [X3] :
( ( leq(X3,X1)
& leq(X3,X0) )
=> leq(X3,X2) )
& leq(X2,X1)
& leq(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X0,X1,X2] :
( ismeetu(X2,X0,X1)
<=> ! [X3] :
( ( leq(X3,X1)
& leq(X3,X0) )
<=> leq(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f29,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f34,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f38,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [A,B,C] :
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f47,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0] : multiplication(X0,omega(X0)) = omega(X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f49,plain,
! [A,B,C] :
( leq(A,addition(omega(B),multiplication(star(B),C)))
| ~ leq(A,addition(multiplication(B,A),C)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f50,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f52,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X1,sK0_skl(X0))],[f52]) ).
fof(f54,plain,
! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f57,plain,
( ! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ! [X0,X1] :
( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( multiplication(X1,X0) = zero
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( multiplication(X0,X1) = zero
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f61,plain,
! [X0,X1] :
( addition(X1,X0) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f62,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f63,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f68,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( c(addition(X0,X1)) = multiplication(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
! [X0,X1] :
( c(addition(X0,X1)) = multiplication(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f72,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ~ leq(X3,X2)
& leq(X3,X1)
& leq(X3,X0) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) )
& ( ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) )
| ~ ismeet(X2,X0,X1) ) ),
inference(NNF_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X3,X2)
& leq(X3,X1)
& leq(X3,X0) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) )
| ~ ismeet(X2,X0,X1) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f76,plain,
( ! [X0,X1,X2] :
( ( ~ leq(sK1_skl(X2,X1,X0),X2)
& leq(sK1_skl(X2,X1,X0),X1)
& leq(sK1_skl(X2,X1,X0),X0) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) )
| ~ ismeet(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X3,sK1_skl(X2,X1,X0))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( leq(X0,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,X1),X1)
| ~ leq(X0,X2)
| ~ leq(X0,X1)
| ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,X1),X2)
| ~ leq(X0,X2)
| ~ leq(X0,X1)
| ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ leq(sK1_skl(X0,X2,X1),X0)
| ~ leq(X0,X2)
| ~ leq(X0,X1)
| ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ismeetu(X2,X0,X1) )
& ( ! [X3] :
( ( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f84,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( ( leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ismeetu(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
( ! [X0,X1,X2] :
( ( ( leq(sK2_skl(X2,X1,X0),X2)
| ( leq(sK2_skl(X2,X1,X0),X1)
& leq(sK2_skl(X2,X1,X0),X0) ) )
& ( ~ leq(sK2_skl(X2,X1,X0),X2)
| ~ leq(sK2_skl(X2,X1,X0),X1)
| ~ leq(sK2_skl(X2,X1,X0),X0) ) )
| ismeetu(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(X3,sK2_skl(X2,X1,X0))],[f84]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X0)
| leq(X3,X1)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X0)
| leq(X3,X2)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ leq(sK2_skl(X0,X2,X1),X0)
| ~ leq(sK2_skl(X0,X2,X1),X2)
| ~ leq(sK2_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
! [X0,X1,X2] :
( leq(sK2_skl(X0,X2,X1),X0)
| leq(sK2_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f91,plain,
! [X0,X1,X2] :
( leq(sK2_skl(X0,X2,X1),X0)
| leq(sK2_skl(X0,X2,X1),X2)
| ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f102,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f29,f27]) ).
fof(f119,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f120,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f121,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f30,f28]) ).
fof(f125,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f126,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f127,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f30,f28]) ).
fof(f129,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f28,f27]) ).
fof(f130,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f27]) ).
fof(f131,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f28,f30]) ).
fof(f135,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f41,f30]) ).
fof(f136,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f41,f102]) ).
fof(f137,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f28,f41]) ).
fof(f139,plain,
! [X0] :
( X0 != zero
| leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f29,f41]) ).
fof(f140,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f27,f41]) ).
fof(f178,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))) = omega(multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f31,f48]) ).
fof(f179,plain,
zero = omega(zero),
inference(paramodulation,[status(thm)],[f37,f48]) ).
fof(f181,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))) = omega(multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f48,f31]) ).
fof(f184,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(X0),X1)) = multiplication(omega(X0),X1),
inference(paramodulation,[status(thm)],[f48,f31]) ).
fof(f189,plain,
! [X0] :
( c(X0) = zero
| complement(sK0_skl(X0),X0) ),
inference(resolution,[status(thm)],[f54,f68]) ).
fof(f190,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f34]) ).
fof(f191,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f34]) ).
fof(f196,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),X1)) = addition(omega(X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f48,f34]) ).
fof(f198,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f32,f34]) ).
fof(f202,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(X0))) = addition(multiplication(X0,X1),omega(X0)),
inference(paramodulation,[status(thm)],[f48,f34]) ).
fof(f204,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f32,f34]) ).
fof(f205,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f34,f41]) ).
fof(f206,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f34,f28]) ).
fof(f207,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f34,f27]) ).
fof(f208,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f27]) ).
fof(f223,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(X0))) = addition(omega(X0),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f27,f202]) ).
fof(f225,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f27,f204]) ).
fof(f229,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f34,f140]) ).
fof(f230,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f28,f140]) ).
fof(f239,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f27,f35]) ).
fof(f240,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f27,f35]) ).
fof(f242,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f31,f35]) ).
fof(f244,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f35]) ).
fof(f245,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = addition(omega(X0),multiplication(X1,omega(X0))),
inference(paramodulation,[status(thm)],[f48,f35]) ).
fof(f248,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f31,f35]) ).
fof(f250,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f33,f35]) ).
fof(f251,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = addition(multiplication(X0,omega(X1)),omega(X1)),
inference(paramodulation,[status(thm)],[f48,f35]) ).
fof(f255,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f35,f140]) ).
fof(f256,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f35,f41]) ).
fof(f257,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f35,f28]) ).
fof(f258,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f35,f27]) ).
fof(f259,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f35,f27]) ).
fof(f267,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f27,f250]) ).
fof(f268,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = addition(omega(X1),multiplication(X0,omega(X1))),
inference(forward_demodulation,[status(thm)],[f27,f251]) ).
fof(f273,plain,
! [X0,X1] :
( c(X0) = zero
| complement(X0,X1)
| c(X0) != X1 ),
inference(resolution,[status(thm)],[f65,f68]) ).
fof(f274,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f127,f41]) ).
fof(f275,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f28,f127]) ).
fof(f279,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f28,f127]) ).
fof(f283,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f27,f127]) ).
fof(f286,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f127,f28]) ).
fof(f288,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f127,f140]) ).
fof(f291,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f28,f275]) ).
fof(f292,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f28,f291]) ).
fof(f297,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f28,f279]) ).
fof(f298,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f28,f297]) ).
fof(f300,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f28,f286]) ).
fof(f301,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f28,f300]) ).
fof(f306,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f35,f274]) ).
fof(f307,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f34,f274]) ).
fof(f308,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f28,f274]) ).
fof(f312,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f274]) ).
fof(f315,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f42,f40]) ).
fof(f316,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f31,f42]) ).
fof(f317,plain,
leq(addition(one,zero),star(zero)),
inference(paramodulation,[status(thm)],[f37,f42]) ).
fof(f318,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f33,f42]) ).
fof(f319,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f28,f315]) ).
fof(f320,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f27,f319]) ).
fof(f321,plain,
leq(one,star(zero)),
inference(forward_demodulation,[status(thm)],[f29,f317]) ).
fof(f322,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f312,f40]) ).
fof(f323,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f35,f312]) ).
fof(f324,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f34,f312]) ).
fof(f325,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f28,f312]) ).
fof(f332,plain,
addition(one,star(zero)) = star(zero),
inference(resolution,[status(thm)],[f321,f40]) ).
fof(f333,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f325,f40]) ).
fof(f334,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f28,f325]) ).
fof(f337,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f27,f325]) ).
fof(f340,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f35,f325]) ).
fof(f341,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f34,f325]) ).
fof(f342,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f28,f325]) ).
fof(f349,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f28,f337]) ).
fof(f351,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f349,f40]) ).
fof(f352,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f28,f349]) ).
fof(f358,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f35,f349]) ).
fof(f359,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f34,f349]) ).
fof(f360,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f28,f349]) ).
fof(f369,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f43,f40]) ).
fof(f371,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f32,f43]) ).
fof(f372,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f28,f369]) ).
fof(f373,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f27,f372]) ).
fof(f375,plain,
! [X0] :
( c(sK0_skl(X0)) = X0
| ~ test(sK0_skl(X0))
| c(X0) = zero ),
inference(resolution,[status(thm)],[f189,f66]) ).
fof(f376,plain,
! [X0] :
( addition(X0,sK0_skl(X0)) = one
| c(X0) = zero ),
inference(resolution,[status(thm)],[f189,f60]) ).
fof(f377,plain,
! [X0] :
( multiplication(sK0_skl(X0),X0) = zero
| c(X0) = zero ),
inference(resolution,[status(thm)],[f189,f59]) ).
fof(f378,plain,
! [X0] :
( multiplication(X0,sK0_skl(X0)) = zero
| c(X0) = zero ),
inference(resolution,[status(thm)],[f189,f58]) ).
fof(f381,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f28,f283]) ).
fof(f386,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f28,f283]) ).
fof(f394,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f283,f28]) ).
fof(f400,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f283,f325]) ).
fof(f401,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f283,f312]) ).
fof(f404,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f283,f140]) ).
fof(f406,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f283,f28]) ).
fof(f408,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f28,f381]) ).
fof(f423,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f28,f394]) ).
fof(f426,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f28,f406]) ).
fof(f427,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f28,f426]) ).
fof(f429,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f35,f401]) ).
fof(f430,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f34,f401]) ).
fof(f431,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f28,f401]) ).
fof(f439,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f35,f401]) ).
fof(f440,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f34,f401]) ).
fof(f441,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f28,f401]) ).
fof(f451,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f35,f429]) ).
fof(f452,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f34,f430]) ).
fof(f460,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f35,f439]) ).
fof(f461,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f34,f440]) ).
fof(f469,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f35,f45]) ).
fof(f470,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f34,f45]) ).
fof(f471,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(X2,multiplication(X0,X1))),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f283,f45]) ).
fof(f472,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(multiplication(X0,X1),X2)),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f127,f45]) ).
fof(f474,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f27,f45]) ).
fof(f475,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f27,f45]) ).
fof(f476,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f30,f45]) ).
fof(f477,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f31,f45]) ).
fof(f478,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f37,f45]) ).
fof(f479,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f33,f45]) ).
fof(f480,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),omega(X0))
| ~ leq(addition(omega(X0),X1),omega(X0)) ),
inference(paramodulation,[status(thm)],[f48,f45]) ).
fof(f481,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f36,f45]) ).
fof(f482,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f32,f45]) ).
fof(f484,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f102,f478]) ).
fof(f485,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f102,f481]) ).
fof(f487,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f322]) ).
fof(f493,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f28,f322]) ).
fof(f499,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f27,f322]) ).
fof(f502,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(X0,multiplication(X1,X2))),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f322,f45]) ).
fof(f503,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f322,f28]) ).
fof(f517,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f322,f140]) ).
fof(f519,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f322,f28]) ).
fof(f524,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f28,f493]) ).
fof(f543,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f28,f519]) ).
fof(f544,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f28,f543]) ).
fof(f546,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f499]) ).
fof(f553,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f499]) ).
fof(f563,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(multiplication(X1,X2),X0)),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f499,f45]) ).
fof(f564,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f499,f28]) ).
fof(f576,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f499,f325]) ).
fof(f580,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f499,f140]) ).
fof(f582,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f499,f28]) ).
fof(f584,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f28,f546]) ).
fof(f590,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f28,f553]) ).
fof(f601,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f28,f564]) ).
fof(f613,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f28,f582]) ).
fof(f614,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f499,f613]) ).
fof(f615,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f28,f614]) ).
fof(f619,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f35,f288]) ).
fof(f620,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f34,f288]) ).
fof(f621,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X0,X1)
| leq(addition(addition(X0,X1),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f28,f288]) ).
fof(f634,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),X2) != multiplication(X0,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f35,f619]) ).
fof(f635,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X1)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f34,f620]) ).
fof(f636,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X0,X1)
| leq(addition(X0,addition(X1,X2)),addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f28,f621]) ).
fof(f647,plain,
( star(zero) != one
| leq(addition(one,star(zero)),one) ),
inference(paramodulation,[status(thm)],[f332,f288]) ).
fof(f653,plain,
! [X0] : leq(one,addition(X0,star(zero))),
inference(paramodulation,[status(thm)],[f332,f349]) ).
fof(f658,plain,
( star(zero) != one
| leq(star(zero),one) ),
inference(paramodulation,[status(thm)],[f332,f140]) ).
fof(f659,plain,
( star(zero) != star(zero)
| leq(one,star(zero)) ),
inference(paramodulation,[status(thm)],[f332,f41]) ).
fof(f660,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(paramodulation,[status(thm)],[f332,f28]) ).
fof(f661,definition,
( sQ0_spl
<=> leq(addition(one,star(zero)),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f662,plain,
( ~ sQ0_spl
| leq(addition(one,star(zero)),one) ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f664,definition,
( sQ1_spl
<=> star(zero) = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( ~ sQ1_spl
| star(zero) = one ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f666,plain,
( sQ1_spl
| star(zero) != one ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f667,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f647,f661,f664]) ).
fof(f677,definition,
( sQ2_spl
<=> leq(star(zero),one) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( ~ sQ2_spl
| leq(star(zero),one) ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f658,f677,f664]) ).
fof(f681,definition,
( sQ3_spl
<=> leq(one,star(zero)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f684,definition,
( sQ4_spl
<=> star(zero) = star(zero) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f686,plain,
( sQ4_spl
| star(zero) != star(zero) ),
inference(component_clause,[status(thm)],[f684]) ).
fof(f687,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f659,f681,f684]) ).
fof(f688,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X1,X2),star(X2)),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f35,f47]) ).
fof(f689,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f34,f47]) ).
fof(f690,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X1,X2),X0),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f499,f47]) ).
fof(f691,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,multiplication(X1,X2)),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f322,f47]) ).
fof(f692,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,multiplication(X0,X1)),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f283,f47]) ).
fof(f693,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f127,f47]) ).
fof(f695,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f27,f47]) ).
fof(f696,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f27,f47]) ).
fof(f697,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f30,f47]) ).
fof(f698,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f31,f47]) ).
fof(f699,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f37,f47]) ).
fof(f700,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f33,f47]) ).
fof(f701,plain,
! [X0,X1] :
( leq(multiplication(X1,star(omega(X0))),X0)
| ~ leq(addition(omega(X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f48,f47]) ).
fof(f702,plain,
! [X0,X1] :
( leq(multiplication(X0,star(zero)),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f36,f47]) ).
fof(f703,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f32,f47]) ).
fof(f704,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f31,f688]) ).
fof(f705,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f31,f689]) ).
fof(f707,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f31,f697]) ).
fof(f708,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f102,f699]) ).
fof(f709,plain,
! [X0,X1] :
( leq(multiplication(X0,star(zero)),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f102,f702]) ).
fof(f710,plain,
! [X0] : addition(one,addition(X0,star(zero))) = addition(X0,star(zero)),
inference(resolution,[status(thm)],[f653,f40]) ).
fof(f712,plain,
! [X0,X1] : leq(one,addition(X0,addition(X1,star(zero)))),
inference(paramodulation,[status(thm)],[f28,f653]) ).
fof(f714,plain,
! [X0] : leq(one,addition(star(zero),X0)),
inference(paramodulation,[status(thm)],[f27,f653]) ).
fof(f717,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(resolution,[status(thm)],[f714,f40]) ).
fof(f729,plain,
( star(zero) != one
| leq(addition(star(zero),one),one) ),
inference(paramodulation,[status(thm)],[f332,f404]) ).
fof(f730,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f35,f404]) ).
fof(f731,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f34,f404]) ).
fof(f732,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(addition(X0,addition(X1,X2)),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f28,f404]) ).
fof(f745,definition,
( sQ5_spl
<=> leq(addition(star(zero),one),one) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f746,plain,
( ~ sQ5_spl
| leq(addition(star(zero),one),one) ),
inference(component_clause,[status(thm)],[f745]) ).
fof(f748,plain,
( ~ sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f729,f745,f664]) ).
fof(f749,plain,
! [X0,X1,X2] :
( multiplication(addition(X1,X0),X2) != multiplication(X1,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f35,f730]) ).
fof(f750,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f34,f731]) ).
fof(f772,plain,
( star(zero) != star(zero)
| leq(addition(one,star(zero)),star(zero)) ),
inference(paramodulation,[status(thm)],[f332,f517]) ).
fof(f773,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f35,f517]) ).
fof(f774,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f34,f517]) ).
fof(f775,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f28,f517]) ).
fof(f797,definition,
( sQ6_spl
<=> leq(addition(one,star(zero)),star(zero)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f800,plain,
( ~ sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f772,f797,f684]) ).
fof(f801,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),X2) != multiplication(X1,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f35,f773]) ).
fof(f802,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f34,f774]) ).
fof(f803,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,addition(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f28,f775]) ).
fof(f815,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f686]) ).
fof(f816,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f815]) ).
fof(f818,plain,
! [X0] : leq(one,addition(omega(X0),multiplication(star(X0),star(zero)))),
inference(resolution,[status(thm)],[f50,f653]) ).
fof(f820,plain,
! [X0,X1,X2] : leq(X0,addition(omega(X1),multiplication(star(X1),addition(X0,X2)))),
inference(resolution,[status(thm)],[f50,f349]) ).
fof(f821,plain,
! [X0,X1,X2] : leq(X0,addition(omega(X1),multiplication(star(X1),addition(X2,X0)))),
inference(resolution,[status(thm)],[f50,f325]) ).
fof(f822,plain,
! [X0,X1] : leq(X0,addition(omega(X1),multiplication(star(X1),X0))),
inference(resolution,[status(thm)],[f50,f312]) ).
fof(f823,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X2,X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f35,f50]) ).
fof(f824,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X2))))
| ~ leq(X0,multiplication(X1,addition(X0,X2))) ),
inference(paramodulation,[status(thm)],[f34,f50]) ).
fof(f825,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),addition(multiplication(X2,X0),X1))))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f499,f50]) ).
fof(f826,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),addition(X1,multiplication(X2,X0)))))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f322,f50]) ).
fof(f827,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),addition(X2,multiplication(X1,X0)))))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f283,f50]) ).
fof(f828,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),addition(multiplication(X1,X0),X2))))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f127,f50]) ).
fof(f829,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f29,f50]) ).
fof(f830,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f27,f50]) ).
fof(f831,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f27,f50]) ).
fof(f832,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f30,f50]) ).
fof(f833,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),X3)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f31,f50]) ).
fof(f834,plain,
! [X0,X1] :
( leq(X0,addition(omega(zero),multiplication(star(zero),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f37,f50]) ).
fof(f835,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),X1)))
| ~ leq(X0,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f33,f50]) ).
fof(f838,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f32,f50]) ).
fof(f839,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),zero))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f36,f829]) ).
fof(f840,plain,
! [X0,X1] :
( leq(X0,omega(X1))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f29,f839]) ).
fof(f841,plain,
! [X0,X1] :
( leq(X0,addition(omega(zero),multiplication(star(zero),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f102,f834]) ).
fof(f842,plain,
! [X0,X1] :
( leq(X0,addition(zero,multiplication(star(zero),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f179,f841]) ).
fof(f843,plain,
! [X0,X1] :
( leq(X0,multiplication(star(zero),X1))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f102,f842]) ).
fof(f844,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(star(one),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f835,f274]) ).
fof(f854,plain,
( star(zero) != star(zero)
| leq(addition(star(zero),one),star(zero)) ),
inference(paramodulation,[status(thm)],[f332,f580]) ).
fof(f855,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f35,f580]) ).
fof(f856,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f34,f580]) ).
fof(f857,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X0
| leq(addition(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f28,f580]) ).
fof(f884,definition,
( sQ7_spl
<=> leq(addition(star(zero),one),star(zero)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f887,plain,
( ~ sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f854,f884,f684]) ).
fof(f888,plain,
! [X0,X1,X2] :
( multiplication(addition(X1,X0),X2) != multiplication(X0,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f35,f855]) ).
fof(f889,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X1)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f34,f856]) ).
fof(f907,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| complement(zero,one) ),
inference(resolution,[status(thm)],[f61,f29]) ).
fof(f908,plain,
( multiplication(one,one) != zero
| multiplication(one,one) != zero
| complement(one,one) ),
inference(resolution,[status(thm)],[f61,f30]) ).
fof(f909,plain,
( multiplication(one,zero) != zero
| multiplication(zero,one) != zero
| complement(one,zero) ),
inference(resolution,[status(thm)],[f61,f102]) ).
fof(f910,plain,
( star(zero) != one
| multiplication(star(zero),one) != zero
| multiplication(one,star(zero)) != zero
| complement(star(zero),one) ),
inference(paramodulation,[status(thm)],[f332,f61]) ).
fof(f911,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != one
| multiplication(multiplication(X0,X1),multiplication(X2,X1)) != zero
| multiplication(multiplication(X2,X1),multiplication(X0,X1)) != zero
| complement(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f35,f61]) ).
fof(f912,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != one
| multiplication(multiplication(X0,X1),multiplication(X0,X2)) != zero
| multiplication(multiplication(X0,X2),multiplication(X0,X1)) != zero
| complement(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f34,f61]) ).
fof(f913,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != one
| multiplication(X0,addition(X1,X2)) != zero
| multiplication(addition(X1,X2),X0) != zero
| complement(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f28,f61]) ).
fof(f914,plain,
! [X0] :
( X0 != one
| multiplication(X0,zero) != zero
| multiplication(zero,X0) != zero
| complement(X0,zero) ),
inference(paramodulation,[status(thm)],[f102,f61]) ).
fof(f915,plain,
! [X0,X1] :
( addition(X1,X0) != one
| multiplication(addition(X0,X1),X0) != zero
| multiplication(X0,addition(X0,X1)) != zero
| complement(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f499,f61]) ).
fof(f916,plain,
! [X0,X1] :
( addition(X0,X1) != one
| multiplication(addition(X0,X1),X1) != zero
| multiplication(X1,addition(X0,X1)) != zero
| complement(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f322,f61]) ).
fof(f917,plain,
! [X0,X1] :
( addition(X1,X0) != one
| multiplication(addition(X0,X1),X1) != zero
| multiplication(X1,addition(X0,X1)) != zero
| complement(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f283,f61]) ).
fof(f918,plain,
! [X0,X1] :
( addition(X0,X1) != one
| multiplication(addition(X0,X1),X0) != zero
| multiplication(X0,addition(X0,X1)) != zero
| complement(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f127,f61]) ).
fof(f919,plain,
! [X0] :
( X0 != one
| multiplication(zero,X0) != zero
| multiplication(X0,zero) != zero
| complement(zero,X0) ),
inference(paramodulation,[status(thm)],[f29,f61]) ).
fof(f920,plain,
! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X0,X1) ),
inference(paramodulation,[status(thm)],[f27,f61]) ).
fof(f921,plain,
! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X0,X1) ),
inference(paramodulation,[status(thm)],[f27,f61]) ).
fof(f922,plain,
! [X0] :
( X0 != one
| multiplication(X0,X0) != zero
| multiplication(X0,X0) != zero
| complement(X0,X0) ),
inference(paramodulation,[status(thm)],[f30,f61]) ).
fof(f923,definition,
( sQ8_spl
<=> complement(zero,one) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( ~ sQ8_spl
| complement(zero,one) ),
inference(component_clause,[status(thm)],[f923]) ).
fof(f926,definition,
( sQ9_spl
<=> multiplication(one,zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f928,plain,
( sQ9_spl
| multiplication(one,zero) != zero ),
inference(component_clause,[status(thm)],[f926]) ).
fof(f929,definition,
( sQ10_spl
<=> multiplication(zero,one) = zero ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f931,plain,
( sQ10_spl
| multiplication(zero,one) != zero ),
inference(component_clause,[status(thm)],[f929]) ).
fof(f932,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f907,f923,f926,f929]) ).
fof(f933,definition,
( sQ11_spl
<=> complement(one,one) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f934,plain,
( ~ sQ11_spl
| complement(one,one) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f935,plain,
( sQ11_spl
| ~ complement(one,one) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f936,definition,
( sQ12_spl
<=> multiplication(one,one) = zero ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f937,plain,
( ~ sQ12_spl
| multiplication(one,one) = zero ),
inference(component_clause,[status(thm)],[f936]) ).
fof(f938,plain,
( sQ12_spl
| multiplication(one,one) != zero ),
inference(component_clause,[status(thm)],[f936]) ).
fof(f939,plain,
( ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f908,f933,f936]) ).
fof(f940,definition,
( sQ13_spl
<=> complement(one,zero) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f941,plain,
( ~ sQ13_spl
| complement(one,zero) ),
inference(component_clause,[status(thm)],[f940]) ).
fof(f943,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f909,f940,f929,f926]) ).
fof(f944,definition,
( sQ14_spl
<=> complement(star(zero),one) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f945,plain,
( ~ sQ14_spl
| complement(star(zero),one) ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f947,definition,
( sQ15_spl
<=> multiplication(one,star(zero)) = zero ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f950,definition,
( sQ16_spl
<=> multiplication(star(zero),one) = zero ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f951,plain,
( ~ sQ16_spl
| multiplication(star(zero),one) = zero ),
inference(component_clause,[status(thm)],[f950]) ).
fof(f952,plain,
( sQ16_spl
| multiplication(star(zero),one) != zero ),
inference(component_clause,[status(thm)],[f950]) ).
fof(f953,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f910,f944,f947,f950,f664]) ).
fof(f954,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != one
| multiplication(multiplication(X0,X1),multiplication(X2,X1)) != zero
| multiplication(X2,multiplication(X1,multiplication(X0,X1))) != zero
| complement(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(forward_demodulation,[status(thm)],[f31,f911]) ).
fof(f955,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != one
| multiplication(X0,multiplication(X1,multiplication(X2,X1))) != zero
| multiplication(X2,multiplication(X1,multiplication(X0,X1))) != zero
| complement(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(forward_demodulation,[status(thm)],[f31,f954]) ).
fof(f956,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != one
| multiplication(multiplication(X0,X1),multiplication(X0,X2)) != zero
| multiplication(X0,multiplication(X2,multiplication(X0,X1))) != zero
| complement(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f31,f912]) ).
fof(f957,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != one
| multiplication(X0,multiplication(X1,multiplication(X0,X2))) != zero
| multiplication(X0,multiplication(X2,multiplication(X0,X1))) != zero
| complement(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f31,f956]) ).
fof(f958,plain,
! [X0] :
( X0 != one
| multiplication(X0,zero) != zero
| zero != zero
| complement(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f914]) ).
fof(f959,plain,
! [X0] :
( X0 != one
| zero != zero
| zero != zero
| complement(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f36,f958]) ).
fof(f960,plain,
! [X0] :
( X0 != one
| zero != zero
| complement(X0,zero) ),
inference(duplicate_literals_removal,[status(thm)],[f959]) ).
fof(f961,plain,
! [X0] :
( X0 != one
| complement(X0,zero) ),
inference(trivial_equality_resolution,[status(thm)],[f960]) ).
fof(f962,plain,
! [X0] :
( X0 != one
| multiplication(zero,X0) != zero
| zero != zero
| complement(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f36,f919]) ).
fof(f963,plain,
! [X0] :
( X0 != one
| zero != zero
| zero != zero
| complement(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f37,f962]) ).
fof(f964,plain,
! [X0] :
( X0 != one
| zero != zero
| complement(zero,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f963]) ).
fof(f965,plain,
! [X0] :
( X0 != one
| complement(zero,X0) ),
inference(trivial_equality_resolution,[status(thm)],[f964]) ).
fof(f966,plain,
! [X0] :
( X0 != one
| multiplication(X0,X0) != zero
| complement(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f922]) ).
fof(f967,plain,
( sQ9_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f33,f928]) ).
fof(f968,plain,
( sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f967]) ).
fof(f969,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f968]) ).
fof(f970,plain,
( sQ10_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f37,f931]) ).
fof(f971,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f970]) ).
fof(f972,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f971]) ).
fof(f973,plain,
( ~ sQ11_spl
| c(one) = one
| ~ test(one) ),
inference(resolution,[status(thm)],[f934,f66]) ).
fof(f975,plain,
( ~ sQ11_spl
| multiplication(one,one) = zero ),
inference(resolution,[status(thm)],[f934,f59]) ).
fof(f976,plain,
( ~ sQ11_spl
| multiplication(one,one) = zero ),
inference(resolution,[status(thm)],[f934,f58]) ).
fof(f977,plain,
( ~ sQ11_spl
| test(one) ),
inference(resolution,[status(thm)],[f934,f55]) ).
fof(f978,definition,
( sQ17_spl
<=> test(one) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f979,plain,
( ~ sQ17_spl
| test(one) ),
inference(component_clause,[status(thm)],[f978]) ).
fof(f980,plain,
( sQ17_spl
| ~ test(one) ),
inference(component_clause,[status(thm)],[f978]) ).
fof(f981,definition,
( sQ18_spl
<=> c(one) = one ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f982,plain,
( ~ sQ18_spl
| c(one) = one ),
inference(component_clause,[status(thm)],[f981]) ).
fof(f983,plain,
( sQ18_spl
| c(one) != one ),
inference(component_clause,[status(thm)],[f981]) ).
fof(f984,plain,
( ~ sQ11_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f973,f978,f981,f933]) ).
fof(f985,plain,
( ~ sQ11_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f33,f975]) ).
fof(f986,plain,
( ~ sQ11_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f33,f976]) ).
fof(f987,plain,
( sQ12_spl
| one != zero ),
inference(forward_demodulation,[status(thm)],[f33,f938]) ).
fof(f988,plain,
( ~ sQ8_spl
| c(zero) = one
| ~ test(zero) ),
inference(resolution,[status(thm)],[f924,f66]) ).
fof(f992,plain,
( ~ sQ8_spl
| test(one) ),
inference(resolution,[status(thm)],[f924,f55]) ).
fof(f993,definition,
( sQ19_spl
<=> test(zero) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f994,plain,
( ~ sQ19_spl
| test(zero) ),
inference(component_clause,[status(thm)],[f993]) ).
fof(f995,plain,
( sQ19_spl
| ~ test(zero) ),
inference(component_clause,[status(thm)],[f993]) ).
fof(f996,definition,
( sQ20_spl
<=> c(zero) = one ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f997,plain,
( ~ sQ20_spl
| c(zero) = one ),
inference(component_clause,[status(thm)],[f996]) ).
fof(f999,plain,
( ~ sQ8_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f988,f993,f996,f923]) ).
fof(f1000,plain,
! [X0] :
( ~ sQ8_spl
| complement(one,X0)
| c(one) != X0 ),
inference(resolution,[status(thm)],[f992,f65]) ).
fof(f1001,plain,
( ~ sQ8_spl
| complement(sK0_skl(one),one) ),
inference(resolution,[status(thm)],[f992,f54]) ).
fof(f1002,plain,
( sQ19_spl
| c(zero) = zero ),
inference(resolution,[status(thm)],[f995,f68]) ).
fof(f1003,plain,
( ~ sQ13_spl
| c(one) = zero
| ~ test(one) ),
inference(resolution,[status(thm)],[f941,f66]) ).
fof(f1007,plain,
( ~ sQ13_spl
| test(zero) ),
inference(resolution,[status(thm)],[f941,f55]) ).
fof(f1008,definition,
( sQ21_spl
<=> c(one) = zero ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1009,plain,
( ~ sQ21_spl
| c(one) = zero ),
inference(component_clause,[status(thm)],[f1008]) ).
fof(f1011,plain,
( ~ sQ13_spl
| sQ21_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1003,f978,f1008,f940]) ).
fof(f1012,plain,
( ~ sQ13_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1007,f995]) ).
fof(f1013,plain,
( ~ sQ13_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f1012]) ).
fof(f1014,plain,
( sQ17_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f980,f992]) ).
fof(f1015,plain,
( sQ17_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1014]) ).
fof(f1016,plain,
! [X0] :
( ~ sQ8_spl
| c(addition(X0,one)) = multiplication(c(X0),c(one))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f70,f992]) ).
fof(f1017,plain,
! [X0,X1] :
( c(X1) = zero
| c(addition(X0,X1)) = multiplication(c(X0),c(X1))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f70,f68]) ).
fof(f1018,plain,
! [X0] :
( ~ sQ13_spl
| c(addition(X0,zero)) = multiplication(c(X0),c(zero))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f1007,f70]) ).
fof(f1019,plain,
! [X0] :
( ~ sQ13_spl
| complement(zero,X0)
| c(zero) != X0 ),
inference(resolution,[status(thm)],[f1007,f65]) ).
fof(f1020,plain,
( ~ sQ13_spl
| complement(sK0_skl(zero),zero) ),
inference(resolution,[status(thm)],[f1007,f54]) ).
fof(f1021,plain,
! [X0] :
( ~ sQ13_spl
| c(X0) = multiplication(c(X0),c(zero))
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f29,f1018]) ).
fof(f1024,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| zero = one ),
inference(forward_demodulation,[status(thm)],[f1009,f982]) ).
fof(f1025,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1024,f987]) ).
fof(f1026,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1025]) ).
fof(f1027,plain,
( ~ sQ12_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f33,f937]) ).
fof(f1028,plain,
( ~ sQ21_spl
| ~ sQ18_spl
| c(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f1024,f1009]) ).
fof(f1029,plain,
( ~ sQ20_spl
| ~ sQ18_spl
| ~ sQ21_spl
| c(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f1024,f997]) ).
fof(f1030,plain,
( ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f1024,f941]) ).
fof(f1031,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ21_spl
| test(zero) ),
inference(backward_demodulation,[status(thm)],[f1024,f992]) ).
fof(f1032,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f1024,f924]) ).
fof(f1036,plain,
( sQ1_spl
| ~ sQ18_spl
| ~ sQ21_spl
| star(zero) != zero ),
inference(backward_demodulation,[status(thm)],[f1024,f666]) ).
fof(f1042,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ21_spl
| multiplication(zero,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1024,f33]) ).
fof(f1048,plain,
! [X0] :
( ~ sQ13_spl
| c(multiplication(X0,zero)) = addition(c(X0),c(zero))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f72,f1007]) ).
fof(f1049,plain,
! [X0,X1] :
( c(X1) = zero
| c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f72,f68]) ).
fof(f1050,plain,
! [X0] :
( ~ sQ13_spl
| c(zero) = addition(c(X0),c(zero))
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f36,f1048]) ).
fof(f1051,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f1024,f934]) ).
fof(f1052,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,zero) ),
inference(forward_demodulation,[status(thm)],[f1024,f1051]) ).
fof(f1053,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| c(zero) = zero
| ~ test(zero) ),
inference(resolution,[status(thm)],[f1052,f66]) ).
fof(f1056,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| test(zero) ),
inference(resolution,[status(thm)],[f1052,f55]) ).
fof(f1057,definition,
( sQ22_spl
<=> c(zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1058,plain,
( ~ sQ22_spl
| c(zero) = zero ),
inference(component_clause,[status(thm)],[f1057]) ).
fof(f1060,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| sQ22_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1053,f993,f1057,f1008,f981,f933]) ).
fof(f1061,plain,
! [X0] :
( ~ sQ8_spl
| c(multiplication(X0,one)) = addition(c(X0),c(one))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f992,f72]) ).
fof(f1062,plain,
! [X0] :
( ~ sQ8_spl
| c(addition(X0,one)) = multiplication(c(X0),c(one))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f992,f70]) ).
fof(f1063,plain,
! [X0] :
( ~ sQ8_spl
| complement(one,X0)
| c(one) != X0 ),
inference(resolution,[status(thm)],[f992,f65]) ).
fof(f1082,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),X1)))
| ~ leq(X0,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f33,f50]) ).
fof(f1083,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f33,f47]) ).
fof(f1084,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f33,f45]) ).
fof(f1085,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f33,f35]) ).
fof(f1086,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f35]) ).
fof(f1091,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(star(one),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f1082,f274]) ).
fof(f1092,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f27,f1085]) ).
fof(f1095,plain,
! [X0,X1,X2] :
( leq(sK1_skl(addition(X0,X1),X2,addition(X1,X0)),addition(X1,X0))
| ~ leq(addition(X0,X1),X2)
| ismeet(addition(X0,X1),addition(X1,X0),X2) ),
inference(resolution,[status(thm)],[f80,f401]) ).
fof(f1096,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X0)
| ~ leq(zero,X1)
| ismeet(zero,X0,X1) ),
inference(resolution,[status(thm)],[f80,f136]) ).
fof(f1097,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(X0,X3,addition(X1,addition(X0,X2))),addition(X1,addition(X0,X2)))
| ~ leq(X0,X3)
| ismeet(X0,addition(X1,addition(X0,X2)),X3) ),
inference(resolution,[status(thm)],[f80,f349]) ).
fof(f1098,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(X0,X3,addition(X1,addition(X2,X0))),addition(X1,addition(X2,X0)))
| ~ leq(X0,X3)
| ismeet(X0,addition(X1,addition(X2,X0)),X3) ),
inference(resolution,[status(thm)],[f80,f325]) ).
fof(f1099,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,addition(X1,X0)),addition(X1,X0))
| ~ leq(X0,X2)
| ismeet(X0,addition(X1,X0),X2) ),
inference(resolution,[status(thm)],[f80,f312]) ).
fof(f1100,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,addition(X0,X1)),addition(X0,X1))
| ~ leq(X0,X2)
| ismeet(X0,addition(X0,X1),X2) ),
inference(resolution,[status(thm)],[f80,f274]) ).
fof(f1101,plain,
! [X0,X1] :
( leq(sK1_skl(X0,X1,X0),X0)
| ~ leq(X0,X1)
| ismeet(X0,X0,X1) ),
inference(resolution,[status(thm)],[f80,f135]) ).
fof(f1102,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X0)
| ismeet(zero,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1096,f136]) ).
fof(f1110,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f32,f50]) ).
fof(f1111,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f32,f47]) ).
fof(f1112,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f32,f45]) ).
fof(f1115,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f32,f34]) ).
fof(f1116,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f32,f34]) ).
fof(f1121,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f27,f1115]) ).
fof(f1122,plain,
( sQ18_spl
| ~ sQ21_spl
| zero != one ),
inference(forward_demodulation,[status(thm)],[f1009,f983]) ).
fof(f1123,plain,
( ~ sQ20_spl
| complement(c(zero),zero) ),
inference(resolution,[status(thm)],[f961,f997]) ).
fof(f1124,plain,
complement(multiplication(one,one),zero),
inference(resolution,[status(thm)],[f961,f33]) ).
fof(f1125,plain,
complement(multiplication(one,one),zero),
inference(resolution,[status(thm)],[f961,f32]) ).
fof(f1126,plain,
complement(addition(one,zero),zero),
inference(resolution,[status(thm)],[f961,f29]) ).
fof(f1127,plain,
complement(addition(one,one),zero),
inference(resolution,[status(thm)],[f961,f30]) ).
fof(f1128,plain,
complement(addition(zero,one),zero),
inference(resolution,[status(thm)],[f961,f102]) ).
fof(f1129,plain,
complement(one,zero),
inference(equality_resolution,[status(thm)],[f961]) ).
fof(f1130,plain,
( ~ sQ20_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f997,f1123]) ).
fof(f1131,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f33,f1124]) ).
fof(f1132,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f33,f1125]) ).
fof(f1133,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f29,f1126]) ).
fof(f1134,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f30,f1127]) ).
fof(f1135,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f102,f1128]) ).
fof(f1136,plain,
( ~ sQ20_spl
| complement(zero,c(zero)) ),
inference(resolution,[status(thm)],[f965,f997]) ).
fof(f1137,plain,
complement(zero,multiplication(one,one)),
inference(resolution,[status(thm)],[f965,f33]) ).
fof(f1138,plain,
complement(zero,multiplication(one,one)),
inference(resolution,[status(thm)],[f965,f32]) ).
fof(f1139,plain,
complement(zero,addition(one,zero)),
inference(resolution,[status(thm)],[f965,f29]) ).
fof(f1140,plain,
complement(zero,addition(one,one)),
inference(resolution,[status(thm)],[f965,f30]) ).
fof(f1141,plain,
complement(zero,addition(zero,one)),
inference(resolution,[status(thm)],[f965,f102]) ).
fof(f1142,plain,
complement(zero,one),
inference(equality_resolution,[status(thm)],[f965]) ).
fof(f1143,plain,
( ~ sQ20_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f997,f1136]) ).
fof(f1144,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f33,f1137]) ).
fof(f1145,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f33,f1138]) ).
fof(f1146,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f29,f1139]) ).
fof(f1147,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f30,f1140]) ).
fof(f1148,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f102,f1141]) ).
fof(f1149,plain,
( ~ sQ8_spl
| c(sK0_skl(one)) = one
| ~ test(sK0_skl(one)) ),
inference(resolution,[status(thm)],[f1001,f66]) ).
fof(f1150,plain,
( ~ sQ8_spl
| multiplication(sK0_skl(one),one) = zero ),
inference(resolution,[status(thm)],[f1001,f59]) ).
fof(f1153,definition,
( sQ23_spl
<=> test(sK0_skl(one)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1154,plain,
( ~ sQ23_spl
| test(sK0_skl(one)) ),
inference(component_clause,[status(thm)],[f1153]) ).
fof(f1155,plain,
( sQ23_spl
| ~ test(sK0_skl(one)) ),
inference(component_clause,[status(thm)],[f1153]) ).
fof(f1156,definition,
( sQ24_spl
<=> c(sK0_skl(one)) = one ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1157,plain,
( ~ sQ24_spl
| c(sK0_skl(one)) = one ),
inference(component_clause,[status(thm)],[f1156]) ).
fof(f1159,plain,
( ~ sQ8_spl
| sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1149,f1153,f1156,f923]) ).
fof(f1160,plain,
( ~ sQ8_spl
| sK0_skl(one) = zero ),
inference(forward_demodulation,[status(thm)],[f32,f1150]) ).
fof(f1162,plain,
! [X0,X1,X2] :
( leq(sK1_skl(addition(X0,X1),X2,addition(X1,X0)),X2)
| ~ leq(addition(X0,X1),X2)
| ismeet(addition(X0,X1),addition(X1,X0),X2) ),
inference(resolution,[status(thm)],[f81,f401]) ).
fof(f1163,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X1)
| ~ leq(zero,X1)
| ismeet(zero,X0,X1) ),
inference(resolution,[status(thm)],[f81,f136]) ).
fof(f1164,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(X0,X3,addition(X1,addition(X0,X2))),X3)
| ~ leq(X0,X3)
| ismeet(X0,addition(X1,addition(X0,X2)),X3) ),
inference(resolution,[status(thm)],[f81,f349]) ).
fof(f1165,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(X0,X3,addition(X1,addition(X2,X0))),X3)
| ~ leq(X0,X3)
| ismeet(X0,addition(X1,addition(X2,X0)),X3) ),
inference(resolution,[status(thm)],[f81,f325]) ).
fof(f1166,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,addition(X1,X0)),X2)
| ~ leq(X0,X2)
| ismeet(X0,addition(X1,X0),X2) ),
inference(resolution,[status(thm)],[f81,f312]) ).
fof(f1167,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,addition(X0,X1)),X2)
| ~ leq(X0,X2)
| ismeet(X0,addition(X0,X1),X2) ),
inference(resolution,[status(thm)],[f81,f274]) ).
fof(f1168,plain,
! [X0,X1] :
( leq(sK1_skl(X0,X1,X0),X1)
| ~ leq(X0,X1)
| ismeet(X0,X0,X1) ),
inference(resolution,[status(thm)],[f81,f135]) ).
fof(f1169,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X1)
| ismeet(zero,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1163,f136]) ).
fof(f1175,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ test(zero) ),
inference(forward_demodulation,[status(thm)],[f1160,f1155]) ).
fof(f1176,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1175,f1007]) ).
fof(f1177,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1176]) ).
fof(f1178,plain,
( ~ sQ24_spl
| ~ sQ8_spl
| c(zero) = one ),
inference(forward_demodulation,[status(thm)],[f1160,f1157]) ).
fof(f1179,plain,
( ~ sQ23_spl
| ~ sQ8_spl
| test(zero) ),
inference(forward_demodulation,[status(thm)],[f1160,f1154]) ).
fof(f1180,plain,
( ~ sQ13_spl
| c(sK0_skl(zero)) = zero
| ~ test(sK0_skl(zero)) ),
inference(resolution,[status(thm)],[f1020,f66]) ).
fof(f1184,definition,
( sQ25_spl
<=> test(sK0_skl(zero)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f1185,plain,
( ~ sQ25_spl
| test(sK0_skl(zero)) ),
inference(component_clause,[status(thm)],[f1184]) ).
fof(f1186,plain,
( sQ25_spl
| ~ test(sK0_skl(zero)) ),
inference(component_clause,[status(thm)],[f1184]) ).
fof(f1187,definition,
( sQ26_spl
<=> c(sK0_skl(zero)) = zero ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1188,plain,
( ~ sQ26_spl
| c(sK0_skl(zero)) = zero ),
inference(component_clause,[status(thm)],[f1187]) ).
fof(f1190,plain,
( ~ sQ13_spl
| sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f1180,f1184,f1187,f940]) ).
fof(f1191,plain,
( sQ25_spl
| c(sK0_skl(zero)) = zero ),
inference(resolution,[status(thm)],[f1186,f68]) ).
fof(f1192,plain,
! [X0] :
( leq(sK1_skl(one,X0,star(zero)),X0)
| ~ leq(one,X0)
| ismeet(one,star(zero),X0) ),
inference(resolution,[status(thm)],[f321,f81]) ).
fof(f1193,plain,
! [X0] :
( leq(sK1_skl(one,X0,star(zero)),star(zero))
| ~ leq(one,X0)
| ismeet(one,star(zero),X0) ),
inference(resolution,[status(thm)],[f321,f80]) ).
fof(f1198,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,X0)
| zero != X0 ),
inference(forward_demodulation,[status(thm)],[f1009,f1000]) ).
fof(f1199,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,omega(zero)) ),
inference(resolution,[status(thm)],[f1198,f179]) ).
fof(f1200,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,addition(zero,zero)) ),
inference(resolution,[status(thm)],[f1198,f102]) ).
fof(f1201,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,sK0_skl(one)) ),
inference(resolution,[status(thm)],[f1198,f1160]) ).
fof(f1202,plain,
( sQ25_spl
| ~ sQ8_spl
| ~ sQ21_spl
| complement(one,c(sK0_skl(zero))) ),
inference(resolution,[status(thm)],[f1198,f1191]) ).
fof(f1203,plain,
( ~ sQ21_spl
| ~ sQ8_spl
| complement(one,c(one)) ),
inference(resolution,[status(thm)],[f1198,f1009]) ).
fof(f1204,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(one,zero)) ),
inference(resolution,[status(thm)],[f1198,f33]) ).
fof(f1205,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(zero,X0)) ),
inference(resolution,[status(thm)],[f1198,f37]) ).
fof(f1206,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(zero,one)) ),
inference(resolution,[status(thm)],[f1198,f32]) ).
fof(f1207,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(X0,zero)) ),
inference(resolution,[status(thm)],[f1198,f36]) ).
fof(f1208,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,addition(zero,zero)) ),
inference(resolution,[status(thm)],[f1198,f29]) ).
fof(f1209,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,addition(zero,zero)) ),
inference(resolution,[status(thm)],[f1198,f30]) ).
fof(f1210,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(equality_resolution,[status(thm)],[f1198]) ).
fof(f1211,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f179,f1199]) ).
fof(f1212,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f102,f1200]) ).
fof(f1213,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f1160,f1201]) ).
fof(f1214,plain,
( sQ25_spl
| ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f1191,f1202]) ).
fof(f1215,plain,
( ~ sQ21_spl
| ~ sQ8_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f1009,f1203]) ).
fof(f1216,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f33,f1204]) ).
fof(f1217,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f1205]) ).
fof(f1218,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f1206]) ).
fof(f1219,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f36,f1207]) ).
fof(f1220,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f102,f1208]) ).
fof(f1221,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f102,f1209]) ).
fof(f1225,plain,
( ~ sQ13_spl
| addition(zero,sK0_skl(zero)) = one ),
inference(resolution,[status(thm)],[f60,f1020]) ).
fof(f1226,plain,
! [X0] :
( c(X0) = zero
| addition(X0,sK0_skl(X0)) = one ),
inference(resolution,[status(thm)],[f60,f189]) ).
fof(f1227,plain,
( ~ sQ13_spl
| sK0_skl(zero) = one ),
inference(forward_demodulation,[status(thm)],[f102,f1225]) ).
fof(f1228,plain,
( sQ25_spl
| ~ sQ13_spl
| c(one) = zero ),
inference(backward_demodulation,[status(thm)],[f1227,f1191]) ).
fof(f1229,plain,
( sQ25_spl
| ~ sQ13_spl
| ~ test(one) ),
inference(backward_demodulation,[status(thm)],[f1227,f1186]) ).
fof(f1231,plain,
( ~ sQ13_spl
| complement(zero,sK0_skl(zero)) ),
inference(resolution,[status(thm)],[f1227,f965]) ).
fof(f1234,plain,
( sQ25_spl
| ~ sQ13_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1229,f978,f940,f1184]) ).
fof(f1235,plain,
( ~ sQ13_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f1227,f1231]) ).
fof(f1238,plain,
( ~ sQ26_spl
| ~ sQ13_spl
| c(one) = zero ),
inference(forward_demodulation,[status(thm)],[f1227,f1188]) ).
fof(f1239,plain,
( ~ sQ25_spl
| ~ sQ13_spl
| test(one) ),
inference(forward_demodulation,[status(thm)],[f1227,f1185]) ).
fof(f1241,plain,
! [X0,X1] :
( leq(sK1_skl(one,X1,addition(star(zero),X0)),X1)
| ~ leq(one,X1)
| ismeet(one,addition(star(zero),X0),X1) ),
inference(resolution,[status(thm)],[f714,f81]) ).
fof(f1242,plain,
! [X0,X1] :
( leq(sK1_skl(one,X1,addition(star(zero),X0)),addition(star(zero),X0))
| ~ leq(one,X1)
| ismeet(one,addition(star(zero),X0),X1) ),
inference(resolution,[status(thm)],[f714,f80]) ).
fof(f1243,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(resolution,[status(thm)],[f714,f40]) ).
fof(f1252,plain,
! [X0] : leq(one,addition(omega(X0),multiplication(star(X0),star(zero)))),
inference(resolution,[status(thm)],[f653,f50]) ).
fof(f1253,plain,
! [X0,X1] :
( leq(sK1_skl(one,X1,addition(X0,star(zero))),X1)
| ~ leq(one,X1)
| ismeet(one,addition(X0,star(zero)),X1) ),
inference(resolution,[status(thm)],[f653,f81]) ).
fof(f1254,plain,
! [X0,X1] :
( leq(sK1_skl(one,X1,addition(X0,star(zero))),addition(X0,star(zero)))
| ~ leq(one,X1)
| ismeet(one,addition(X0,star(zero)),X1) ),
inference(resolution,[status(thm)],[f653,f80]) ).
fof(f1255,plain,
! [X0] : addition(one,addition(X0,star(zero))) = addition(X0,star(zero)),
inference(resolution,[status(thm)],[f653,f40]) ).
fof(f1256,plain,
! [X0,X1] : leq(one,addition(X0,addition(X1,star(zero)))),
inference(paramodulation,[status(thm)],[f28,f653]) ).
fof(f1281,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(paramodulation,[status(thm)],[f332,f28]) ).
fof(f1300,plain,
( ~ sQ20_spl
| c(zero) = zero
| complement(zero,one) ),
inference(resolution,[status(thm)],[f273,f997]) ).
fof(f1302,plain,
! [X0] :
( c(X0) = zero
| complement(X0,addition(zero,c(X0))) ),
inference(resolution,[status(thm)],[f273,f102]) ).
fof(f1303,plain,
! [X0] :
( c(X0) = zero
| complement(X0,multiplication(one,c(X0))) ),
inference(resolution,[status(thm)],[f273,f33]) ).
fof(f1304,plain,
! [X0] :
( c(X0) = zero
| complement(X0,multiplication(c(X0),one)) ),
inference(resolution,[status(thm)],[f273,f32]) ).
fof(f1305,plain,
! [X0] :
( c(X0) = zero
| complement(X0,addition(c(X0),zero)) ),
inference(resolution,[status(thm)],[f273,f29]) ).
fof(f1306,plain,
! [X0] :
( c(X0) = zero
| complement(X0,addition(c(X0),c(X0))) ),
inference(resolution,[status(thm)],[f273,f30]) ).
fof(f1307,plain,
! [X0] :
( ~ sQ20_spl
| c(zero) = zero
| complement(zero,X0)
| one != X0 ),
inference(paramodulation,[status(thm)],[f997,f273]) ).
fof(f1309,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(equality_resolution,[status(thm)],[f273]) ).
fof(f1310,plain,
( ~ sQ20_spl
| sQ22_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f1300,f923,f1057,f996]) ).
fof(f1312,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f102,f1302]) ).
fof(f1313,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f33,f1303]) ).
fof(f1314,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f32,f1304]) ).
fof(f1315,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f29,f1305]) ).
fof(f1316,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f1306]) ).
fof(f1317,definition,
! [X0] :
( sQ27_spl
<=> ( complement(zero,X0)
| one != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1318,plain,
! [X0] :
( ~ sQ27_spl
| complement(zero,X0)
| one != X0 ),
inference(component_clause,[status(thm)],[f1317]) ).
fof(f1320,plain,
( ~ sQ20_spl
| sQ22_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f1307,f1317,f1057,f996]) ).
fof(f1325,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| zero = one ),
inference(backward_demodulation,[status(thm)],[f1058,f997]) ).
fof(f1328,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| ~ sQ22_spl
| complement(one,c(zero)) ),
inference(resolution,[status(thm)],[f1058,f1198]) ).
fof(f1330,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1325,f987]) ).
fof(f1331,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1330]) ).
fof(f1337,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| ~ sQ22_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f1058,f1328]) ).
fof(f1345,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ22_spl
| sK0_skl(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f1325,f1227]) ).
fof(f1346,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ22_spl
| addition(X1,X0) = zero
| ~ complement(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f1325,f60]) ).
fof(f1347,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,X0)
| zero != X0 ),
inference(backward_demodulation,[status(thm)],[f1325,f1198]) ).
fof(f1349,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ22_spl
| sK0_skl(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f1325,f1160]) ).
fof(f1350,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| X0 != zero
| complement(zero,X0) ),
inference(backward_demodulation,[status(thm)],[f1325,f965]) ).
fof(f1351,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| X0 != zero
| complement(X0,zero) ),
inference(backward_demodulation,[status(thm)],[f1325,f961]) ).
fof(f1352,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| multiplication(X0,zero) = X0 ),
inference(backward_demodulation,[status(thm)],[f1325,f32]) ).
fof(f1353,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| multiplication(zero,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1325,f33]) ).
fof(f1354,plain,
( sQ1_spl
| ~ sQ20_spl
| ~ sQ22_spl
| star(zero) != zero ),
inference(backward_demodulation,[status(thm)],[f1325,f666]) ).
fof(f1355,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f1325,f924]) ).
fof(f1356,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f1325,f941]) ).
fof(f1358,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ22_spl
| test(zero) ),
inference(backward_demodulation,[status(thm)],[f1325,f992]) ).
fof(f1364,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| test(zero) ),
inference(resolution,[status(thm)],[f1052,f55]) ).
fof(f1366,plain,
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f1325,f934]) ).
fof(f1367,plain,
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,zero) ),
inference(forward_demodulation,[status(thm)],[f1325,f1366]) ).
fof(f1368,plain,
! [X0] :
( ~ leq(sK2_skl(X0,X0,X0),X0)
| ~ leq(sK2_skl(X0,X0,X0),X0)
| ismeetu(X0,X0,X0)
| ismeetu(X0,X0,X0) ),
inference(resolution,[status(thm)],[f90,f89]) ).
fof(f1370,plain,
! [X0,X1,X2] :
( leq(sK1_skl(sK2_skl(X0,X1,X0),X2,X0),X2)
| ~ leq(sK2_skl(X0,X1,X0),X2)
| ismeet(sK2_skl(X0,X1,X0),X0,X2)
| ismeetu(X0,X0,X1) ),
inference(resolution,[status(thm)],[f90,f81]) ).
fof(f1371,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X1),X3)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X1,X3)
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f90,f81]) ).
fof(f1372,plain,
! [X0,X1,X2] :
( leq(sK1_skl(sK2_skl(X0,X1,X0),X2,X0),X0)
| ~ leq(sK2_skl(X0,X1,X0),X2)
| ismeet(sK2_skl(X0,X1,X0),X0,X2)
| ismeetu(X0,X0,X1) ),
inference(resolution,[status(thm)],[f90,f80]) ).
fof(f1373,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X1),X1)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X1,X3)
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f90,f80]) ).
fof(f1374,plain,
! [X0,X1] :
( addition(sK2_skl(X0,X1,X0),X0) = X0
| ismeetu(X0,X0,X1) ),
inference(resolution,[status(thm)],[f90,f40]) ).
fof(f1375,plain,
! [X0,X1,X2] :
( addition(sK2_skl(X0,X2,X1),X1) = X1
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f90,f40]) ).
fof(f1377,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X0),X3)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X0,X3)
| leq(sK2_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f90,f81]) ).
fof(f1378,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X0),X0)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X0,X3)
| leq(sK2_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f90,f80]) ).
fof(f1379,plain,
! [X0,X1,X2] :
( addition(sK2_skl(X0,X2,X1),X0) = X0
| leq(sK2_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f90,f40]) ).
fof(f1380,plain,
! [X0] :
( ~ leq(sK2_skl(X0,X0,X0),X0)
| ismeetu(X0,X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1368]) ).
fof(f1381,plain,
! [X0,X1] :
( addition(X0,sK2_skl(X0,X1,X0)) = X0
| ismeetu(X0,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f27,f1374]) ).
fof(f1382,plain,
! [X0,X1,X2] :
( addition(X1,sK2_skl(X0,X2,X1)) = X1
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f27,f1375]) ).
fof(f1383,plain,
! [X0,X1,X2] :
( addition(X0,sK2_skl(X0,X2,X1)) = X0
| leq(sK2_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f27,f1379]) ).
fof(f1386,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ21_spl
| zero = X0 ),
inference(paramodulation,[status(thm)],[f37,f1042]) ).
fof(f1410,plain,
( sQ1_spl
| ~ sQ18_spl
| ~ sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1036,f1386]) ).
fof(f1418,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f1386,f1386]) ).
fof(f1422,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ21_spl
| ~ sQ13_spl
| test(X0) ),
inference(paramodulation,[status(thm)],[f1386,f1007]) ).
fof(f1423,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f1386,f136]) ).
fof(f1426,plain,
( sQ1_spl
| ~ sQ18_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1410]) ).
fof(f1431,plain,
( ~ sQ5_spl
| leq(addition(one,star(zero)),one) ),
inference(forward_demodulation,[status(thm)],[f27,f746]) ).
fof(f1432,plain,
( sQ16_spl
| ~ sQ18_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f952,f1386]) ).
fof(f1433,plain,
( sQ16_spl
| ~ sQ18_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1432]) ).
fof(f1441,plain,
! [X0,X1] :
( ~ leq(sK2_skl(X0,X0,X1),X0)
| ~ leq(sK2_skl(X0,X0,X1),X1)
| ismeetu(X0,X1,X0)
| ismeetu(X0,X1,X0) ),
inference(resolution,[status(thm)],[f91,f89]) ).
fof(f1443,plain,
! [X0,X1,X2] :
( leq(sK1_skl(sK2_skl(X0,X0,X1),X2,X0),X2)
| ~ leq(sK2_skl(X0,X0,X1),X2)
| ismeet(sK2_skl(X0,X0,X1),X0,X2)
| ismeetu(X0,X1,X0) ),
inference(resolution,[status(thm)],[f91,f81]) ).
fof(f1444,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X2),X3)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X2,X3)
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f91,f81]) ).
fof(f1445,plain,
! [X0,X1,X2] :
( leq(sK1_skl(sK2_skl(X0,X0,X1),X2,X0),X0)
| ~ leq(sK2_skl(X0,X0,X1),X2)
| ismeet(sK2_skl(X0,X0,X1),X0,X2)
| ismeetu(X0,X1,X0) ),
inference(resolution,[status(thm)],[f91,f80]) ).
fof(f1446,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X2),X2)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X2,X3)
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f91,f80]) ).
fof(f1448,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X0),X3)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X0,X3)
| leq(sK2_skl(X0,X2,X1),X2)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f91,f81]) ).
fof(f1449,plain,
! [X0,X1,X2,X3] :
( leq(sK1_skl(sK2_skl(X0,X2,X1),X3,X0),X0)
| ~ leq(sK2_skl(X0,X2,X1),X3)
| ismeet(sK2_skl(X0,X2,X1),X0,X3)
| leq(sK2_skl(X0,X2,X1),X2)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f91,f80]) ).
fof(f1454,plain,
! [X0,X1] :
( ~ leq(sK2_skl(X0,X0,X1),X0)
| ~ leq(sK2_skl(X0,X0,X1),X1)
| ismeetu(X0,X1,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1441]) ).
fof(f1456,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ~ leq(sK2_skl(X0,X2,X1),X2)
| ~ leq(sK2_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f89,f1423]) ).
fof(f1457,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ~ leq(sK1_skl(X0,X2,X1),X0)
| ~ leq(X0,X1)
| ismeet(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f82,f1423]) ).
fof(f1458,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ~ leq(sK2_skl(X0,X2,X1),X2)
| ismeetu(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1456,f1423]) ).
fof(f1459,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ~ leq(sK1_skl(X0,X2,X1),X0)
| ismeet(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1457,f1423]) ).
fof(f1460,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| addition(X1,X0) != one
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f1418]) ).
fof(f1461,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(resolution,[status(thm)],[f1460,f1418]) ).
fof(f1463,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| X2 != one
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(paramodulation,[status(thm)],[f1418,f1460]) ).
fof(f1465,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| complement(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1461,f1418]) ).
fof(f1467,definition,
! [X0,X1] :
( sQ31_spl
<=> ( multiplication(X0,X1) != zero
| complement(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1468,plain,
! [X0,X1] :
( ~ sQ31_spl
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(component_clause,[status(thm)],[f1467]) ).
fof(f1470,definition,
! [X2] :
( sQ32_spl
<=> X2 != one ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1473,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f1463,f1467,f1470,f1008,f981]) ).
fof(f1476,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ismeetu(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1458,f1423]) ).
fof(f1477,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ismeet(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1459,f1423]) ).
fof(model,axiom,
( sQ0_spl
| sQ1_spl
| sQ2_spl
| sQ3_spl
| sQ4_spl
| sQ5_spl
| sQ6_spl
| sQ7_spl
| sQ8_spl
| sQ9_spl
| sQ10_spl
| sQ11_spl
| sQ12_spl
| sQ13_spl
| sQ14_spl
| sQ16_spl
| sQ17_spl
| sQ18_spl
| sQ19_spl
| sQ20_spl
| sQ21_spl
| sQ22_spl
| sQ23_spl
| sQ24_spl
| sQ25_spl
| sQ26_spl
| sQ31_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE179+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:52:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.64 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.13/0.64 % SZS output start Saturation for theBenchmark
% See solution above
% 0.13/0.66 % Elapsed time: 0.293574 seconds
% 0.13/0.66 % CPU time: 2.103711 seconds
% 0.13/0.66 % Total memory used: 31.429 MB
% 0.13/0.66 % Net memory used: 29.125 MB
%------------------------------------------------------------------------------