%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE176+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:58:28 PM UTC 2026
% Result : Satisfiable 0.18s 0.57s
% Output : Saturation 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,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/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X0,X1,X2] :
( ismeetu(X2,X0,X1)
<=> ! [X3] :
( ( leq(X3,X1)
& leq(X3,X0) )
<=> leq(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f35,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f41,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f42,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(f43,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,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(f45,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,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))],[f47]) ).
fof(f49,plain,
! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,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)],[f18]) ).
fof(f52,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)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( multiplication(X1,X0) = zero
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( multiplication(X0,X1) = zero
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( addition(X1,X0) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f58,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f63,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( c(addition(X0,X1)) = multiplication(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f65,plain,
! [X0,X1] :
( c(addition(X0,X1)) = multiplication(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f67,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,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)],[f23]) ).
fof(f69,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)],[f68]) ).
fof(f70,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)],[f69]) ).
fof(f71,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))],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( leq(X0,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f75,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)],[f71]) ).
fof(f76,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)],[f71]) ).
fof(f77,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)],[f71]) ).
fof(f78,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)],[f24]) ).
fof(f79,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)],[f78]) ).
fof(f80,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))],[f79]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X0)
| leq(X3,X1)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X0)
| leq(X3,X2)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,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)],[f80]) ).
fof(f85,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)],[f80]) ).
fof(f86,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)],[f80]) ).
fof(f97,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f27,f25]) ).
fof(f114,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f115,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f116,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f28,f26]) ).
fof(f120,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f121,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f122,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f28,f26]) ).
fof(f124,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f26,f25]) ).
fof(f125,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f25]) ).
fof(f126,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f130,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f39,f28]) ).
fof(f131,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f39,f97]) ).
fof(f132,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f134,plain,
! [X0] :
( X0 != zero
| leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f27,f39]) ).
fof(f135,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f25,f39]) ).
fof(f173,plain,
! [X0] :
( c(X0) = zero
| complement(sK0_skl(X0),X0) ),
inference(resolution,[status(thm)],[f49,f63]) ).
fof(f177,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f26,f135]) ).
fof(f185,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f32]) ).
fof(f186,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f32]) ).
fof(f192,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f32]) ).
fof(f197,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f30,f32]) ).
fof(f198,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f32,f135]) ).
fof(f199,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f32,f39]) ).
fof(f200,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)],[f32,f26]) ).
fof(f201,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f32,f25]) ).
fof(f202,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f32,f25]) ).
fof(f218,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f197]) ).
fof(f219,plain,
! [X0,X1] :
( c(X0) = zero
| complement(X0,X1)
| c(X0) != X1 ),
inference(resolution,[status(thm)],[f60,f63]) ).
fof(f221,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f25,f33]) ).
fof(f222,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f25,f33]) ).
fof(f224,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)],[f29,f33]) ).
fof(f226,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f31,f33]) ).
fof(f229,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)],[f29,f33]) ).
fof(f231,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f31,f33]) ).
fof(f235,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f33,f135]) ).
fof(f236,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f33,f39]) ).
fof(f237,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)],[f33,f26]) ).
fof(f238,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f33,f25]) ).
fof(f239,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f33,f25]) ).
fof(f247,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f231]) ).
fof(f252,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f122,f39]) ).
fof(f253,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f26,f122]) ).
fof(f257,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f26,f122]) ).
fof(f261,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f25,f122]) ).
fof(f264,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f122,f26]) ).
fof(f266,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f122,f135]) ).
fof(f269,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f26,f253]) ).
fof(f270,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f26,f269]) ).
fof(f275,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f26,f257]) ).
fof(f276,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f26,f275]) ).
fof(f278,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f26,f264]) ).
fof(f279,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f26,f278]) ).
fof(f284,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f33,f252]) ).
fof(f285,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f32,f252]) ).
fof(f286,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f26,f252]) ).
fof(f290,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f25,f252]) ).
fof(f293,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f290,f38]) ).
fof(f294,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f33,f290]) ).
fof(f295,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f32,f290]) ).
fof(f296,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f26,f290]) ).
fof(f303,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f296,f38]) ).
fof(f304,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f26,f296]) ).
fof(f307,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f25,f296]) ).
fof(f310,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f33,f296]) ).
fof(f311,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f32,f296]) ).
fof(f312,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f26,f296]) ).
fof(f319,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f26,f307]) ).
fof(f321,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f40,f38]) ).
fof(f322,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f29,f40]) ).
fof(f323,plain,
leq(addition(one,zero),star(zero)),
inference(paramodulation,[status(thm)],[f35,f40]) ).
fof(f324,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f31,f40]) ).
fof(f325,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f26,f321]) ).
fof(f326,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f25,f325]) ).
fof(f327,plain,
leq(one,star(zero)),
inference(forward_demodulation,[status(thm)],[f27,f323]) ).
fof(f328,plain,
addition(one,star(zero)) = star(zero),
inference(resolution,[status(thm)],[f327,f38]) ).
fof(f329,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f319,f38]) ).
fof(f330,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f26,f319]) ).
fof(f336,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f33,f319]) ).
fof(f337,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f32,f319]) ).
fof(f338,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f26,f319]) ).
fof(f347,plain,
! [X0] :
( c(sK0_skl(X0)) = X0
| ~ test(sK0_skl(X0))
| c(X0) = zero ),
inference(resolution,[status(thm)],[f173,f61]) ).
fof(f348,plain,
! [X0] :
( addition(X0,sK0_skl(X0)) = one
| c(X0) = zero ),
inference(resolution,[status(thm)],[f173,f55]) ).
fof(f349,plain,
! [X0] :
( multiplication(sK0_skl(X0),X0) = zero
| c(X0) = zero ),
inference(resolution,[status(thm)],[f173,f54]) ).
fof(f350,plain,
! [X0] :
( multiplication(X0,sK0_skl(X0)) = zero
| c(X0) = zero ),
inference(resolution,[status(thm)],[f173,f53]) ).
fof(f352,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f41,f38]) ).
fof(f354,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f30,f41]) ).
fof(f355,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f26,f352]) ).
fof(f356,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f25,f355]) ).
fof(f359,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f26,f261]) ).
fof(f364,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f26,f261]) ).
fof(f372,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f261,f26]) ).
fof(f378,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f261,f296]) ).
fof(f379,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f261,f290]) ).
fof(f382,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f261,f135]) ).
fof(f384,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f261,f26]) ).
fof(f386,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f26,f359]) ).
fof(f401,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f26,f372]) ).
fof(f404,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f26,f384]) ).
fof(f405,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f26,f404]) ).
fof(f407,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f33,f379]) ).
fof(f408,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f32,f379]) ).
fof(f409,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f26,f379]) ).
fof(f417,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f33,f379]) ).
fof(f418,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f32,f379]) ).
fof(f419,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f26,f379]) ).
fof(f429,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f33,f407]) ).
fof(f430,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f32,f408]) ).
fof(f438,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f33,f417]) ).
fof(f439,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f32,f418]) ).
fof(f448,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f293]) ).
fof(f454,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f26,f293]) ).
fof(f460,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f25,f293]) ).
fof(f463,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f293,f26]) ).
fof(f477,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f293,f135]) ).
fof(f479,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f293,f26]) ).
fof(f484,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f26,f454]) ).
fof(f503,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f26,f479]) ).
fof(f504,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f26,f503]) ).
fof(f506,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f460]) ).
fof(f513,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f460]) ).
fof(f523,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f460,f26]) ).
fof(f535,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f460,f296]) ).
fof(f539,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f460,f135]) ).
fof(f541,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f460,f26]) ).
fof(f543,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f26,f506]) ).
fof(f549,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f26,f513]) ).
fof(f560,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f26,f523]) ).
fof(f572,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f26,f541]) ).
fof(f573,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f460,f572]) ).
fof(f574,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f26,f573]) ).
fof(f575,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f33,f43]) ).
fof(f576,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f32,f43]) ).
fof(f577,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)],[f460,f43]) ).
fof(f578,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)],[f293,f43]) ).
fof(f579,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)],[f261,f43]) ).
fof(f580,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)],[f122,f43]) ).
fof(f582,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f25,f43]) ).
fof(f583,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f25,f43]) ).
fof(f584,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f28,f43]) ).
fof(f585,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)],[f29,f43]) ).
fof(f586,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f35,f43]) ).
fof(f587,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f31,f43]) ).
fof(f588,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f34,f43]) ).
fof(f589,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f30,f43]) ).
fof(f591,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f97,f586]) ).
fof(f592,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f97,f588]) ).
fof(f596,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)],[f33,f266]) ).
fof(f597,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)],[f32,f266]) ).
fof(f598,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)],[f26,f266]) ).
fof(f611,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)],[f33,f596]) ).
fof(f612,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)],[f32,f597]) ).
fof(f613,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)],[f26,f598]) ).
fof(f624,plain,
( star(zero) != one
| leq(addition(one,star(zero)),one) ),
inference(paramodulation,[status(thm)],[f328,f266]) ).
fof(f630,plain,
! [X0] : leq(one,addition(X0,star(zero))),
inference(paramodulation,[status(thm)],[f328,f319]) ).
fof(f635,plain,
( star(zero) != one
| leq(star(zero),one) ),
inference(paramodulation,[status(thm)],[f328,f135]) ).
fof(f636,plain,
( star(zero) != star(zero)
| leq(one,star(zero)) ),
inference(paramodulation,[status(thm)],[f328,f39]) ).
fof(f637,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(paramodulation,[status(thm)],[f328,f26]) ).
fof(f638,definition,
( sQ0_spl
<=> leq(addition(one,star(zero)),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( ~ sQ0_spl
| leq(addition(one,star(zero)),one) ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f641,definition,
( sQ1_spl
<=> star(zero) = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( ~ sQ1_spl
| star(zero) = one ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f643,plain,
( sQ1_spl
| star(zero) != one ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f644,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f624,f638,f641]) ).
fof(f654,definition,
( sQ2_spl
<=> leq(star(zero),one) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( ~ sQ2_spl
| leq(star(zero),one) ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f657,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f635,f654,f641]) ).
fof(f658,definition,
( sQ3_spl
<=> leq(one,star(zero)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f661,definition,
( sQ4_spl
<=> star(zero) = star(zero) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( sQ4_spl
| star(zero) != star(zero) ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f664,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f636,f658,f661]) ).
fof(f665,plain,
! [X0] : addition(one,addition(X0,star(zero))) = addition(X0,star(zero)),
inference(resolution,[status(thm)],[f630,f38]) ).
fof(f667,plain,
! [X0,X1] : leq(one,addition(X0,addition(X1,star(zero)))),
inference(paramodulation,[status(thm)],[f26,f630]) ).
fof(f669,plain,
! [X0] : leq(one,addition(star(zero),X0)),
inference(paramodulation,[status(thm)],[f25,f630]) ).
fof(f672,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(resolution,[status(thm)],[f669,f38]) ).
fof(f681,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X1,X2),star(X2)),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f33,f45]) ).
fof(f682,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f32,f45]) ).
fof(f683,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)],[f460,f45]) ).
fof(f684,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)],[f293,f45]) ).
fof(f685,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)],[f261,f45]) ).
fof(f686,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)],[f122,f45]) ).
fof(f688,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f25,f45]) ).
fof(f689,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f25,f45]) ).
fof(f690,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f28,f45]) ).
fof(f691,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)],[f29,f45]) ).
fof(f692,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f35,f45]) ).
fof(f693,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f31,f45]) ).
fof(f694,plain,
! [X0,X1] :
( leq(multiplication(X0,star(zero)),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f34,f45]) ).
fof(f695,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f30,f45]) ).
fof(f696,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f29,f681]) ).
fof(f697,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f29,f682]) ).
fof(f699,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f29,f690]) ).
fof(f700,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f97,f692]) ).
fof(f701,plain,
! [X0,X1] :
( leq(multiplication(X0,star(zero)),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f97,f694]) ).
fof(f705,plain,
( star(zero) != one
| leq(addition(star(zero),one),one) ),
inference(paramodulation,[status(thm)],[f328,f382]) ).
fof(f706,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)],[f33,f382]) ).
fof(f707,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)],[f32,f382]) ).
fof(f708,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)],[f26,f382]) ).
fof(f721,definition,
( sQ5_spl
<=> leq(addition(star(zero),one),one) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f722,plain,
( ~ sQ5_spl
| leq(addition(star(zero),one),one) ),
inference(component_clause,[status(thm)],[f721]) ).
fof(f724,plain,
( ~ sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f705,f721,f641]) ).
fof(f725,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)],[f33,f706]) ).
fof(f726,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)],[f32,f707]) ).
fof(f748,plain,
( star(zero) != star(zero)
| leq(addition(one,star(zero)),star(zero)) ),
inference(paramodulation,[status(thm)],[f328,f477]) ).
fof(f749,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)],[f33,f477]) ).
fof(f750,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)],[f32,f477]) ).
fof(f751,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f26,f477]) ).
fof(f773,definition,
( sQ6_spl
<=> leq(addition(one,star(zero)),star(zero)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( ~ sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f748,f773,f661]) ).
fof(f777,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)],[f33,f749]) ).
fof(f778,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)],[f32,f750]) ).
fof(f779,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,addition(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f26,f751]) ).
fof(f791,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f663]) ).
fof(f792,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f791]) ).
fof(f802,plain,
( star(zero) != star(zero)
| leq(addition(star(zero),one),star(zero)) ),
inference(paramodulation,[status(thm)],[f328,f539]) ).
fof(f803,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)],[f33,f539]) ).
fof(f804,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)],[f32,f539]) ).
fof(f805,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X0
| leq(addition(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f26,f539]) ).
fof(f832,definition,
( sQ7_spl
<=> leq(addition(star(zero),one),star(zero)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f835,plain,
( ~ sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f802,f832,f661]) ).
fof(f836,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)],[f33,f803]) ).
fof(f837,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)],[f32,f804]) ).
fof(f855,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| complement(zero,one) ),
inference(resolution,[status(thm)],[f56,f27]) ).
fof(f856,plain,
( multiplication(one,one) != zero
| multiplication(one,one) != zero
| complement(one,one) ),
inference(resolution,[status(thm)],[f56,f28]) ).
fof(f857,plain,
( multiplication(one,zero) != zero
| multiplication(zero,one) != zero
| complement(one,zero) ),
inference(resolution,[status(thm)],[f56,f97]) ).
fof(f858,plain,
( star(zero) != one
| multiplication(star(zero),one) != zero
| multiplication(one,star(zero)) != zero
| complement(star(zero),one) ),
inference(paramodulation,[status(thm)],[f328,f56]) ).
fof(f859,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)],[f33,f56]) ).
fof(f860,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)],[f32,f56]) ).
fof(f861,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)],[f26,f56]) ).
fof(f862,plain,
! [X0] :
( X0 != one
| multiplication(X0,zero) != zero
| multiplication(zero,X0) != zero
| complement(X0,zero) ),
inference(paramodulation,[status(thm)],[f97,f56]) ).
fof(f863,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)],[f460,f56]) ).
fof(f864,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)],[f293,f56]) ).
fof(f865,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)],[f261,f56]) ).
fof(f866,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)],[f122,f56]) ).
fof(f867,plain,
! [X0] :
( X0 != one
| multiplication(zero,X0) != zero
| multiplication(X0,zero) != zero
| complement(zero,X0) ),
inference(paramodulation,[status(thm)],[f27,f56]) ).
fof(f868,plain,
! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X0,X1) ),
inference(paramodulation,[status(thm)],[f25,f56]) ).
fof(f869,plain,
! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X0,X1) ),
inference(paramodulation,[status(thm)],[f25,f56]) ).
fof(f870,plain,
! [X0] :
( X0 != one
| multiplication(X0,X0) != zero
| multiplication(X0,X0) != zero
| complement(X0,X0) ),
inference(paramodulation,[status(thm)],[f28,f56]) ).
fof(f871,definition,
( sQ8_spl
<=> complement(zero,one) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f872,plain,
( ~ sQ8_spl
| complement(zero,one) ),
inference(component_clause,[status(thm)],[f871]) ).
fof(f874,definition,
( sQ9_spl
<=> multiplication(one,zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f876,plain,
( sQ9_spl
| multiplication(one,zero) != zero ),
inference(component_clause,[status(thm)],[f874]) ).
fof(f877,definition,
( sQ10_spl
<=> multiplication(zero,one) = zero ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f879,plain,
( sQ10_spl
| multiplication(zero,one) != zero ),
inference(component_clause,[status(thm)],[f877]) ).
fof(f880,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f855,f871,f874,f877]) ).
fof(f881,definition,
( sQ11_spl
<=> complement(one,one) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( ~ sQ11_spl
| complement(one,one) ),
inference(component_clause,[status(thm)],[f881]) ).
fof(f883,plain,
( sQ11_spl
| ~ complement(one,one) ),
inference(component_clause,[status(thm)],[f881]) ).
fof(f884,definition,
( sQ12_spl
<=> multiplication(one,one) = zero ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f885,plain,
( ~ sQ12_spl
| multiplication(one,one) = zero ),
inference(component_clause,[status(thm)],[f884]) ).
fof(f886,plain,
( sQ12_spl
| multiplication(one,one) != zero ),
inference(component_clause,[status(thm)],[f884]) ).
fof(f887,plain,
( ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f856,f881,f884]) ).
fof(f888,definition,
( sQ13_spl
<=> complement(one,zero) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f889,plain,
( ~ sQ13_spl
| complement(one,zero) ),
inference(component_clause,[status(thm)],[f888]) ).
fof(f891,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f857,f888,f877,f874]) ).
fof(f892,definition,
( sQ14_spl
<=> complement(star(zero),one) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f893,plain,
( ~ sQ14_spl
| complement(star(zero),one) ),
inference(component_clause,[status(thm)],[f892]) ).
fof(f895,definition,
( sQ15_spl
<=> multiplication(one,star(zero)) = zero ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f898,definition,
( sQ16_spl
<=> multiplication(star(zero),one) = zero ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f899,plain,
( ~ sQ16_spl
| multiplication(star(zero),one) = zero ),
inference(component_clause,[status(thm)],[f898]) ).
fof(f900,plain,
( sQ16_spl
| multiplication(star(zero),one) != zero ),
inference(component_clause,[status(thm)],[f898]) ).
fof(f901,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f858,f892,f895,f898,f641]) ).
fof(f902,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)],[f29,f859]) ).
fof(f903,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)],[f29,f902]) ).
fof(f904,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)],[f29,f860]) ).
fof(f905,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)],[f29,f904]) ).
fof(f906,plain,
! [X0] :
( X0 != one
| multiplication(X0,zero) != zero
| zero != zero
| complement(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f35,f862]) ).
fof(f907,plain,
! [X0] :
( X0 != one
| zero != zero
| zero != zero
| complement(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f34,f906]) ).
fof(f908,plain,
! [X0] :
( X0 != one
| zero != zero
| complement(X0,zero) ),
inference(duplicate_literals_removal,[status(thm)],[f907]) ).
fof(f909,plain,
! [X0] :
( X0 != one
| complement(X0,zero) ),
inference(trivial_equality_resolution,[status(thm)],[f908]) ).
fof(f910,plain,
! [X0] :
( X0 != one
| multiplication(zero,X0) != zero
| zero != zero
| complement(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f34,f867]) ).
fof(f911,plain,
! [X0] :
( X0 != one
| zero != zero
| zero != zero
| complement(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f35,f910]) ).
fof(f912,plain,
! [X0] :
( X0 != one
| zero != zero
| complement(zero,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f911]) ).
fof(f913,plain,
! [X0] :
( X0 != one
| complement(zero,X0) ),
inference(trivial_equality_resolution,[status(thm)],[f912]) ).
fof(f914,plain,
! [X0] :
( X0 != one
| multiplication(X0,X0) != zero
| complement(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f870]) ).
fof(f915,plain,
( sQ9_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f31,f876]) ).
fof(f916,plain,
( sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f915]) ).
fof(f917,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f916]) ).
fof(f918,plain,
( sQ10_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f35,f879]) ).
fof(f919,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f918]) ).
fof(f920,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f919]) ).
fof(f921,plain,
( ~ sQ11_spl
| c(one) = one
| ~ test(one) ),
inference(resolution,[status(thm)],[f882,f61]) ).
fof(f923,plain,
( ~ sQ11_spl
| multiplication(one,one) = zero ),
inference(resolution,[status(thm)],[f882,f54]) ).
fof(f924,plain,
( ~ sQ11_spl
| multiplication(one,one) = zero ),
inference(resolution,[status(thm)],[f882,f53]) ).
fof(f925,plain,
( ~ sQ11_spl
| test(one) ),
inference(resolution,[status(thm)],[f882,f50]) ).
fof(f926,definition,
( sQ17_spl
<=> test(one) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( ~ sQ17_spl
| test(one) ),
inference(component_clause,[status(thm)],[f926]) ).
fof(f928,plain,
( sQ17_spl
| ~ test(one) ),
inference(component_clause,[status(thm)],[f926]) ).
fof(f929,definition,
( sQ18_spl
<=> c(one) = one ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( ~ sQ18_spl
| c(one) = one ),
inference(component_clause,[status(thm)],[f929]) ).
fof(f931,plain,
( sQ18_spl
| c(one) != one ),
inference(component_clause,[status(thm)],[f929]) ).
fof(f932,plain,
( ~ sQ11_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f921,f926,f929,f881]) ).
fof(f933,plain,
( ~ sQ11_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f31,f923]) ).
fof(f934,plain,
( ~ sQ11_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f31,f924]) ).
fof(f935,plain,
( sQ12_spl
| one != zero ),
inference(forward_demodulation,[status(thm)],[f31,f886]) ).
fof(f936,plain,
( ~ sQ8_spl
| c(zero) = one
| ~ test(zero) ),
inference(resolution,[status(thm)],[f872,f61]) ).
fof(f940,plain,
( ~ sQ8_spl
| test(one) ),
inference(resolution,[status(thm)],[f872,f50]) ).
fof(f941,definition,
( sQ19_spl
<=> test(zero) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( ~ sQ19_spl
| test(zero) ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f943,plain,
( sQ19_spl
| ~ test(zero) ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f944,definition,
( sQ20_spl
<=> c(zero) = one ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f945,plain,
( ~ sQ20_spl
| c(zero) = one ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f947,plain,
( ~ sQ8_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f936,f941,f944,f871]) ).
fof(f948,plain,
! [X0] :
( ~ sQ8_spl
| complement(one,X0)
| c(one) != X0 ),
inference(resolution,[status(thm)],[f940,f60]) ).
fof(f949,plain,
( ~ sQ8_spl
| complement(sK0_skl(one),one) ),
inference(resolution,[status(thm)],[f940,f49]) ).
fof(f950,plain,
( sQ19_spl
| c(zero) = zero ),
inference(resolution,[status(thm)],[f943,f63]) ).
fof(f951,plain,
( ~ sQ13_spl
| c(one) = zero
| ~ test(one) ),
inference(resolution,[status(thm)],[f889,f61]) ).
fof(f955,plain,
( ~ sQ13_spl
| test(zero) ),
inference(resolution,[status(thm)],[f889,f50]) ).
fof(f956,definition,
( sQ21_spl
<=> c(one) = zero ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f957,plain,
( ~ sQ21_spl
| c(one) = zero ),
inference(component_clause,[status(thm)],[f956]) ).
fof(f959,plain,
( ~ sQ13_spl
| sQ21_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f951,f926,f956,f888]) ).
fof(f960,plain,
( ~ sQ13_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f955,f943]) ).
fof(f961,plain,
( ~ sQ13_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f960]) ).
fof(f962,plain,
( sQ17_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f928,f940]) ).
fof(f963,plain,
( sQ17_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f964,plain,
! [X0] :
( ~ sQ8_spl
| c(addition(X0,one)) = multiplication(c(X0),c(one))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f65,f940]) ).
fof(f965,plain,
! [X0,X1] :
( c(X1) = zero
| c(addition(X0,X1)) = multiplication(c(X0),c(X1))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f65,f63]) ).
fof(f966,plain,
! [X0] :
( ~ sQ13_spl
| c(addition(X0,zero)) = multiplication(c(X0),c(zero))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f955,f65]) ).
fof(f967,plain,
! [X0] :
( ~ sQ13_spl
| complement(zero,X0)
| c(zero) != X0 ),
inference(resolution,[status(thm)],[f955,f60]) ).
fof(f968,plain,
( ~ sQ13_spl
| complement(sK0_skl(zero),zero) ),
inference(resolution,[status(thm)],[f955,f49]) ).
fof(f969,plain,
! [X0] :
( ~ sQ13_spl
| c(X0) = multiplication(c(X0),c(zero))
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f27,f966]) ).
fof(f972,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| zero = one ),
inference(forward_demodulation,[status(thm)],[f957,f930]) ).
fof(f973,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f935]) ).
fof(f974,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f973]) ).
fof(f975,plain,
( ~ sQ12_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f31,f885]) ).
fof(f976,plain,
( ~ sQ21_spl
| ~ sQ18_spl
| c(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f972,f957]) ).
fof(f977,plain,
( ~ sQ20_spl
| ~ sQ18_spl
| ~ sQ21_spl
| c(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f972,f945]) ).
fof(f978,plain,
( ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f972,f889]) ).
fof(f979,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ21_spl
| test(zero) ),
inference(backward_demodulation,[status(thm)],[f972,f940]) ).
fof(f980,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f972,f872]) ).
fof(f984,plain,
( sQ1_spl
| ~ sQ18_spl
| ~ sQ21_spl
| star(zero) != zero ),
inference(backward_demodulation,[status(thm)],[f972,f643]) ).
fof(f990,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ21_spl
| multiplication(zero,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f972,f31]) ).
fof(f996,plain,
! [X0] :
( ~ sQ13_spl
| c(multiplication(X0,zero)) = addition(c(X0),c(zero))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f67,f955]) ).
fof(f997,plain,
! [X0,X1] :
( c(X1) = zero
| c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f67,f63]) ).
fof(f998,plain,
! [X0] :
( ~ sQ13_spl
| c(zero) = addition(c(X0),c(zero))
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f34,f996]) ).
fof(f999,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f972,f882]) ).
fof(f1000,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| complement(zero,zero) ),
inference(forward_demodulation,[status(thm)],[f972,f999]) ).
fof(f1001,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| c(zero) = zero
| ~ test(zero) ),
inference(resolution,[status(thm)],[f1000,f61]) ).
fof(f1004,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| test(zero) ),
inference(resolution,[status(thm)],[f1000,f50]) ).
fof(f1005,definition,
( sQ22_spl
<=> c(zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1006,plain,
( ~ sQ22_spl
| c(zero) = zero ),
inference(component_clause,[status(thm)],[f1005]) ).
fof(f1008,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| sQ22_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1001,f941,f1005,f956,f929,f881]) ).
fof(f1009,plain,
! [X0] :
( ~ sQ8_spl
| c(multiplication(X0,one)) = addition(c(X0),c(one))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f940,f67]) ).
fof(f1010,plain,
! [X0] :
( ~ sQ8_spl
| c(addition(X0,one)) = multiplication(c(X0),c(one))
| ~ test(X0) ),
inference(resolution,[status(thm)],[f940,f65]) ).
fof(f1011,plain,
! [X0] :
( ~ sQ8_spl
| complement(one,X0)
| c(one) != X0 ),
inference(resolution,[status(thm)],[f940,f60]) ).
fof(f1028,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f31,f45]) ).
fof(f1029,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f31,f43]) ).
fof(f1030,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f31,f33]) ).
fof(f1031,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f31,f33]) ).
fof(f1036,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f1030]) ).
fof(f1039,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)],[f75,f379]) ).
fof(f1040,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X0)
| ~ leq(zero,X1)
| ismeet(zero,X0,X1) ),
inference(resolution,[status(thm)],[f75,f131]) ).
fof(f1041,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)],[f75,f319]) ).
fof(f1042,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)],[f75,f296]) ).
fof(f1043,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)],[f75,f290]) ).
fof(f1044,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)],[f75,f252]) ).
fof(f1045,plain,
! [X0,X1] :
( leq(sK1_skl(X0,X1,X0),X0)
| ~ leq(X0,X1)
| ismeet(X0,X0,X1) ),
inference(resolution,[status(thm)],[f75,f130]) ).
fof(f1046,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X0)
| ismeet(zero,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1040,f131]) ).
fof(f1054,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f30,f45]) ).
fof(f1055,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f30,f43]) ).
fof(f1058,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f30,f32]) ).
fof(f1059,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f32]) ).
fof(f1064,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f1058]) ).
fof(f1065,plain,
( sQ18_spl
| ~ sQ21_spl
| zero != one ),
inference(forward_demodulation,[status(thm)],[f957,f931]) ).
fof(f1066,plain,
( ~ sQ20_spl
| complement(c(zero),zero) ),
inference(resolution,[status(thm)],[f909,f945]) ).
fof(f1067,plain,
complement(multiplication(one,one),zero),
inference(resolution,[status(thm)],[f909,f31]) ).
fof(f1068,plain,
complement(multiplication(one,one),zero),
inference(resolution,[status(thm)],[f909,f30]) ).
fof(f1069,plain,
complement(addition(one,zero),zero),
inference(resolution,[status(thm)],[f909,f27]) ).
fof(f1070,plain,
complement(addition(one,one),zero),
inference(resolution,[status(thm)],[f909,f28]) ).
fof(f1071,plain,
complement(addition(zero,one),zero),
inference(resolution,[status(thm)],[f909,f97]) ).
fof(f1072,plain,
complement(one,zero),
inference(equality_resolution,[status(thm)],[f909]) ).
fof(f1073,plain,
( ~ sQ20_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f945,f1066]) ).
fof(f1074,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f31,f1067]) ).
fof(f1075,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f31,f1068]) ).
fof(f1076,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f27,f1069]) ).
fof(f1077,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f28,f1070]) ).
fof(f1078,plain,
complement(one,zero),
inference(forward_demodulation,[status(thm)],[f97,f1071]) ).
fof(f1079,plain,
( ~ sQ20_spl
| complement(zero,c(zero)) ),
inference(resolution,[status(thm)],[f913,f945]) ).
fof(f1080,plain,
complement(zero,multiplication(one,one)),
inference(resolution,[status(thm)],[f913,f31]) ).
fof(f1081,plain,
complement(zero,multiplication(one,one)),
inference(resolution,[status(thm)],[f913,f30]) ).
fof(f1082,plain,
complement(zero,addition(one,zero)),
inference(resolution,[status(thm)],[f913,f27]) ).
fof(f1083,plain,
complement(zero,addition(one,one)),
inference(resolution,[status(thm)],[f913,f28]) ).
fof(f1084,plain,
complement(zero,addition(zero,one)),
inference(resolution,[status(thm)],[f913,f97]) ).
fof(f1085,plain,
complement(zero,one),
inference(equality_resolution,[status(thm)],[f913]) ).
fof(f1086,plain,
( ~ sQ20_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f945,f1079]) ).
fof(f1087,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f31,f1080]) ).
fof(f1088,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f31,f1081]) ).
fof(f1089,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f27,f1082]) ).
fof(f1090,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f28,f1083]) ).
fof(f1091,plain,
complement(zero,one),
inference(forward_demodulation,[status(thm)],[f97,f1084]) ).
fof(f1092,plain,
( ~ sQ8_spl
| c(sK0_skl(one)) = one
| ~ test(sK0_skl(one)) ),
inference(resolution,[status(thm)],[f949,f61]) ).
fof(f1093,plain,
( ~ sQ8_spl
| multiplication(sK0_skl(one),one) = zero ),
inference(resolution,[status(thm)],[f949,f54]) ).
fof(f1096,definition,
( sQ23_spl
<=> test(sK0_skl(one)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1097,plain,
( ~ sQ23_spl
| test(sK0_skl(one)) ),
inference(component_clause,[status(thm)],[f1096]) ).
fof(f1098,plain,
( sQ23_spl
| ~ test(sK0_skl(one)) ),
inference(component_clause,[status(thm)],[f1096]) ).
fof(f1099,definition,
( sQ24_spl
<=> c(sK0_skl(one)) = one ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1100,plain,
( ~ sQ24_spl
| c(sK0_skl(one)) = one ),
inference(component_clause,[status(thm)],[f1099]) ).
fof(f1102,plain,
( ~ sQ8_spl
| sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1092,f1096,f1099,f871]) ).
fof(f1103,plain,
( ~ sQ8_spl
| sK0_skl(one) = zero ),
inference(forward_demodulation,[status(thm)],[f30,f1093]) ).
fof(f1105,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)],[f76,f379]) ).
fof(f1106,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X1)
| ~ leq(zero,X1)
| ismeet(zero,X0,X1) ),
inference(resolution,[status(thm)],[f76,f131]) ).
fof(f1107,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)],[f76,f319]) ).
fof(f1108,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)],[f76,f296]) ).
fof(f1109,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)],[f76,f290]) ).
fof(f1110,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)],[f76,f252]) ).
fof(f1111,plain,
! [X0,X1] :
( leq(sK1_skl(X0,X1,X0),X1)
| ~ leq(X0,X1)
| ismeet(X0,X0,X1) ),
inference(resolution,[status(thm)],[f76,f130]) ).
fof(f1112,plain,
! [X0,X1] :
( leq(sK1_skl(zero,X1,X0),X1)
| ismeet(zero,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1106,f131]) ).
fof(f1118,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ test(zero) ),
inference(forward_demodulation,[status(thm)],[f1103,f1098]) ).
fof(f1119,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1118,f955]) ).
fof(f1120,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1119]) ).
fof(f1121,plain,
( ~ sQ24_spl
| ~ sQ8_spl
| c(zero) = one ),
inference(forward_demodulation,[status(thm)],[f1103,f1100]) ).
fof(f1122,plain,
( ~ sQ23_spl
| ~ sQ8_spl
| test(zero) ),
inference(forward_demodulation,[status(thm)],[f1103,f1097]) ).
fof(f1123,plain,
( ~ sQ13_spl
| c(sK0_skl(zero)) = zero
| ~ test(sK0_skl(zero)) ),
inference(resolution,[status(thm)],[f968,f61]) ).
fof(f1127,definition,
( sQ25_spl
<=> test(sK0_skl(zero)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f1128,plain,
( ~ sQ25_spl
| test(sK0_skl(zero)) ),
inference(component_clause,[status(thm)],[f1127]) ).
fof(f1129,plain,
( sQ25_spl
| ~ test(sK0_skl(zero)) ),
inference(component_clause,[status(thm)],[f1127]) ).
fof(f1130,definition,
( sQ26_spl
<=> c(sK0_skl(zero)) = zero ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1131,plain,
( ~ sQ26_spl
| c(sK0_skl(zero)) = zero ),
inference(component_clause,[status(thm)],[f1130]) ).
fof(f1133,plain,
( ~ sQ13_spl
| sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f1123,f1127,f1130,f888]) ).
fof(f1134,plain,
( sQ25_spl
| c(sK0_skl(zero)) = zero ),
inference(resolution,[status(thm)],[f1129,f63]) ).
fof(f1135,plain,
! [X0] :
( leq(sK1_skl(one,X0,star(zero)),X0)
| ~ leq(one,X0)
| ismeet(one,star(zero),X0) ),
inference(resolution,[status(thm)],[f327,f76]) ).
fof(f1136,plain,
! [X0] :
( leq(sK1_skl(one,X0,star(zero)),star(zero))
| ~ leq(one,X0)
| ismeet(one,star(zero),X0) ),
inference(resolution,[status(thm)],[f327,f75]) ).
fof(f1141,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,X0)
| zero != X0 ),
inference(forward_demodulation,[status(thm)],[f957,f948]) ).
fof(f1142,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,addition(zero,zero)) ),
inference(resolution,[status(thm)],[f1141,f97]) ).
fof(f1143,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,sK0_skl(one)) ),
inference(resolution,[status(thm)],[f1141,f1103]) ).
fof(f1144,plain,
( sQ25_spl
| ~ sQ8_spl
| ~ sQ21_spl
| complement(one,c(sK0_skl(zero))) ),
inference(resolution,[status(thm)],[f1141,f1134]) ).
fof(f1145,plain,
( ~ sQ21_spl
| ~ sQ8_spl
| complement(one,c(one)) ),
inference(resolution,[status(thm)],[f1141,f957]) ).
fof(f1146,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(one,zero)) ),
inference(resolution,[status(thm)],[f1141,f31]) ).
fof(f1147,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(zero,X0)) ),
inference(resolution,[status(thm)],[f1141,f35]) ).
fof(f1148,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(zero,one)) ),
inference(resolution,[status(thm)],[f1141,f30]) ).
fof(f1149,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,multiplication(X0,zero)) ),
inference(resolution,[status(thm)],[f1141,f34]) ).
fof(f1150,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,addition(zero,zero)) ),
inference(resolution,[status(thm)],[f1141,f27]) ).
fof(f1151,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,addition(zero,zero)) ),
inference(resolution,[status(thm)],[f1141,f28]) ).
fof(f1152,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(equality_resolution,[status(thm)],[f1141]) ).
fof(f1153,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f97,f1142]) ).
fof(f1154,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f1103,f1143]) ).
fof(f1155,plain,
( sQ25_spl
| ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f1134,f1144]) ).
fof(f1156,plain,
( ~ sQ21_spl
| ~ sQ8_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f957,f1145]) ).
fof(f1157,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f31,f1146]) ).
fof(f1158,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f35,f1147]) ).
fof(f1159,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f35,f1148]) ).
fof(f1160,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f34,f1149]) ).
fof(f1161,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f97,f1150]) ).
fof(f1162,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f97,f1151]) ).
fof(f1166,plain,
( ~ sQ13_spl
| addition(zero,sK0_skl(zero)) = one ),
inference(resolution,[status(thm)],[f55,f968]) ).
fof(f1167,plain,
! [X0] :
( c(X0) = zero
| addition(X0,sK0_skl(X0)) = one ),
inference(resolution,[status(thm)],[f55,f173]) ).
fof(f1168,plain,
( ~ sQ13_spl
| sK0_skl(zero) = one ),
inference(forward_demodulation,[status(thm)],[f97,f1166]) ).
fof(f1169,plain,
( sQ25_spl
| ~ sQ13_spl
| c(one) = zero ),
inference(backward_demodulation,[status(thm)],[f1168,f1134]) ).
fof(f1170,plain,
( sQ25_spl
| ~ sQ13_spl
| ~ test(one) ),
inference(backward_demodulation,[status(thm)],[f1168,f1129]) ).
fof(f1172,plain,
( ~ sQ13_spl
| complement(zero,sK0_skl(zero)) ),
inference(resolution,[status(thm)],[f1168,f913]) ).
fof(f1175,plain,
( sQ25_spl
| ~ sQ13_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1170,f926,f888,f1127]) ).
fof(f1176,plain,
( ~ sQ13_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f1168,f1172]) ).
fof(f1179,plain,
( ~ sQ26_spl
| ~ sQ13_spl
| c(one) = zero ),
inference(forward_demodulation,[status(thm)],[f1168,f1131]) ).
fof(f1180,plain,
( ~ sQ25_spl
| ~ sQ13_spl
| test(one) ),
inference(forward_demodulation,[status(thm)],[f1168,f1128]) ).
fof(f1182,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)],[f669,f76]) ).
fof(f1183,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)],[f669,f75]) ).
fof(f1184,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(resolution,[status(thm)],[f669,f38]) ).
fof(f1193,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)],[f630,f76]) ).
fof(f1194,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)],[f630,f75]) ).
fof(f1195,plain,
! [X0] : addition(one,addition(X0,star(zero))) = addition(X0,star(zero)),
inference(resolution,[status(thm)],[f630,f38]) ).
fof(f1196,plain,
! [X0,X1] : leq(one,addition(X0,addition(X1,star(zero)))),
inference(paramodulation,[status(thm)],[f26,f630]) ).
fof(f1221,plain,
! [X0] : addition(one,addition(star(zero),X0)) = addition(star(zero),X0),
inference(paramodulation,[status(thm)],[f328,f26]) ).
fof(f1240,plain,
( ~ sQ20_spl
| c(zero) = zero
| complement(zero,one) ),
inference(resolution,[status(thm)],[f219,f945]) ).
fof(f1242,plain,
! [X0] :
( c(X0) = zero
| complement(X0,addition(zero,c(X0))) ),
inference(resolution,[status(thm)],[f219,f97]) ).
fof(f1243,plain,
! [X0] :
( c(X0) = zero
| complement(X0,multiplication(one,c(X0))) ),
inference(resolution,[status(thm)],[f219,f31]) ).
fof(f1244,plain,
! [X0] :
( c(X0) = zero
| complement(X0,multiplication(c(X0),one)) ),
inference(resolution,[status(thm)],[f219,f30]) ).
fof(f1245,plain,
! [X0] :
( c(X0) = zero
| complement(X0,addition(c(X0),zero)) ),
inference(resolution,[status(thm)],[f219,f27]) ).
fof(f1246,plain,
! [X0] :
( c(X0) = zero
| complement(X0,addition(c(X0),c(X0))) ),
inference(resolution,[status(thm)],[f219,f28]) ).
fof(f1247,plain,
! [X0] :
( ~ sQ20_spl
| c(zero) = zero
| complement(zero,X0)
| one != X0 ),
inference(paramodulation,[status(thm)],[f945,f219]) ).
fof(f1249,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(equality_resolution,[status(thm)],[f219]) ).
fof(f1250,plain,
( ~ sQ20_spl
| sQ22_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f1240,f871,f1005,f944]) ).
fof(f1252,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f1242]) ).
fof(f1253,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f31,f1243]) ).
fof(f1254,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f1244]) ).
fof(f1255,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f27,f1245]) ).
fof(f1256,plain,
! [X0] :
( c(X0) = zero
| complement(X0,c(X0)) ),
inference(forward_demodulation,[status(thm)],[f28,f1246]) ).
fof(f1257,definition,
! [X0] :
( sQ27_spl
<=> ( complement(zero,X0)
| one != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1258,plain,
! [X0] :
( ~ sQ27_spl
| complement(zero,X0)
| one != X0 ),
inference(component_clause,[status(thm)],[f1257]) ).
fof(f1260,plain,
( ~ sQ20_spl
| sQ22_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f1247,f1257,f1005,f944]) ).
fof(f1265,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| zero = one ),
inference(backward_demodulation,[status(thm)],[f1006,f945]) ).
fof(f1268,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| ~ sQ22_spl
| complement(one,c(zero)) ),
inference(resolution,[status(thm)],[f1006,f1141]) ).
fof(f1270,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1265,f935]) ).
fof(f1271,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1270]) ).
fof(f1277,plain,
( ~ sQ8_spl
| ~ sQ21_spl
| ~ sQ22_spl
| complement(one,zero) ),
inference(forward_demodulation,[status(thm)],[f1006,f1268]) ).
fof(f1285,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ22_spl
| sK0_skl(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f1265,f1168]) ).
fof(f1286,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ22_spl
| addition(X1,X0) = zero
| ~ complement(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f1265,f55]) ).
fof(f1287,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,X0)
| zero != X0 ),
inference(backward_demodulation,[status(thm)],[f1265,f1141]) ).
fof(f1289,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ22_spl
| sK0_skl(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f1265,f1103]) ).
fof(f1290,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| X0 != zero
| complement(zero,X0) ),
inference(backward_demodulation,[status(thm)],[f1265,f913]) ).
fof(f1291,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| X0 != zero
| complement(X0,zero) ),
inference(backward_demodulation,[status(thm)],[f1265,f909]) ).
fof(f1292,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| multiplication(X0,zero) = X0 ),
inference(backward_demodulation,[status(thm)],[f1265,f30]) ).
fof(f1293,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ22_spl
| multiplication(zero,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1265,f31]) ).
fof(f1294,plain,
( sQ1_spl
| ~ sQ20_spl
| ~ sQ22_spl
| star(zero) != zero ),
inference(backward_demodulation,[status(thm)],[f1265,f643]) ).
fof(f1295,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f1265,f872]) ).
fof(f1296,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f1265,f889]) ).
fof(f1298,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ22_spl
| test(zero) ),
inference(backward_demodulation,[status(thm)],[f1265,f940]) ).
fof(f1301,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)],[f85,f84]) ).
fof(f1303,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)],[f85,f76]) ).
fof(f1304,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)],[f85,f76]) ).
fof(f1305,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)],[f85,f75]) ).
fof(f1306,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)],[f85,f75]) ).
fof(f1307,plain,
! [X0,X1] :
( addition(sK2_skl(X0,X1,X0),X0) = X0
| ismeetu(X0,X0,X1) ),
inference(resolution,[status(thm)],[f85,f38]) ).
fof(f1308,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)],[f85,f38]) ).
fof(f1310,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)],[f85,f76]) ).
fof(f1311,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)],[f85,f75]) ).
fof(f1312,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)],[f85,f38]) ).
fof(f1313,plain,
! [X0] :
( ~ leq(sK2_skl(X0,X0,X0),X0)
| ismeetu(X0,X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1301]) ).
fof(f1314,plain,
! [X0,X1] :
( addition(X0,sK2_skl(X0,X1,X0)) = X0
| ismeetu(X0,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f25,f1307]) ).
fof(f1315,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)],[f25,f1308]) ).
fof(f1316,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)],[f25,f1312]) ).
fof(f1320,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ21_spl
| test(zero) ),
inference(resolution,[status(thm)],[f1000,f50]) ).
fof(f1322,plain,
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,one) ),
inference(forward_demodulation,[status(thm)],[f1265,f882]) ).
fof(f1323,plain,
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ22_spl
| complement(zero,zero) ),
inference(forward_demodulation,[status(thm)],[f1265,f1322]) ).
fof(f1326,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ21_spl
| zero = X0 ),
inference(paramodulation,[status(thm)],[f35,f990]) ).
fof(f1344,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)],[f86,f84]) ).
fof(f1346,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)],[f86,f76]) ).
fof(f1347,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)],[f86,f76]) ).
fof(f1348,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)],[f86,f75]) ).
fof(f1349,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)],[f86,f75]) ).
fof(f1350,plain,
! [X0,X1] :
( addition(sK2_skl(X0,X0,X1),X0) = X0
| ismeetu(X0,X1,X0) ),
inference(resolution,[status(thm)],[f86,f38]) ).
fof(f1351,plain,
! [X0,X1,X2] :
( addition(sK2_skl(X0,X2,X1),X2) = X2
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f86,f38]) ).
fof(f1353,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)],[f86,f76]) ).
fof(f1354,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)],[f86,f75]) ).
fof(f1355,plain,
! [X0,X1,X2] :
( addition(sK2_skl(X0,X2,X1),X0) = X0
| leq(sK2_skl(X0,X2,X1),X2)
| ismeetu(X0,X1,X2) ),
inference(resolution,[status(thm)],[f86,f38]) ).
fof(f1356,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)],[f1344]) ).
fof(f1357,plain,
! [X0,X1] :
( addition(X0,sK2_skl(X0,X0,X1)) = X0
| ismeetu(X0,X1,X0) ),
inference(forward_demodulation,[status(thm)],[f25,f1350]) ).
fof(f1358,plain,
! [X0,X1,X2] :
( addition(X2,sK2_skl(X0,X2,X1)) = X2
| leq(sK2_skl(X0,X2,X1),X0)
| ismeetu(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f25,f1351]) ).
fof(f1359,plain,
! [X0,X1,X2] :
( addition(X0,sK2_skl(X0,X2,X1)) = X0
| leq(sK2_skl(X0,X2,X1),X2)
| ismeetu(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f25,f1355]) ).
fof(f1360,plain,
( sQ1_spl
| ~ sQ18_spl
| ~ sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f984,f1326]) ).
fof(f1368,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f1326,f1326]) ).
fof(f1372,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ21_spl
| ~ sQ13_spl
| test(X0) ),
inference(paramodulation,[status(thm)],[f1326,f955]) ).
fof(f1373,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f1326,f131]) ).
fof(f1376,plain,
( sQ1_spl
| ~ sQ18_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1360]) ).
fof(f1381,plain,
( ~ sQ5_spl
| leq(addition(one,star(zero)),one) ),
inference(forward_demodulation,[status(thm)],[f25,f722]) ).
fof(f1382,plain,
( sQ16_spl
| ~ sQ18_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f900,f1326]) ).
fof(f1383,plain,
( sQ16_spl
| ~ sQ18_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1382]) ).
fof(f1392,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)],[f84,f1373]) ).
fof(f1393,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)],[f77,f1373]) ).
fof(f1394,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)],[f1392,f1373]) ).
fof(f1395,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)],[f1393,f1373]) ).
fof(f1396,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| addition(X1,X0) != one
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f1368]) ).
fof(f1397,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(resolution,[status(thm)],[f1396,f1368]) ).
fof(f1399,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| X2 != one
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(paramodulation,[status(thm)],[f1368,f1396]) ).
fof(f1401,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ21_spl
| complement(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1397,f1368]) ).
fof(f1403,definition,
! [X0,X1] :
( sQ31_spl
<=> ( multiplication(X0,X1) != zero
| complement(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1404,plain,
! [X0,X1] :
( ~ sQ31_spl
| multiplication(X0,X1) != zero
| complement(X0,X1) ),
inference(component_clause,[status(thm)],[f1403]) ).
fof(f1406,definition,
! [X2] :
( sQ32_spl
<=> X2 != one ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1409,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f1399,f1403,f1406,f956,f929]) ).
fof(f1412,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ismeetu(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1394,f1373]) ).
fof(f1413,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ21_spl
| ismeet(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1395,f1373]) ).
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
% 0.00/0.03 % Problem : KLE176+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n019.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 20 22:49:35 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.41 % Drodi V4.1.1
% 0.18/0.57 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.18/0.57 % SZS output start Saturation for theBenchmark
% See solution above
% 0.18/0.59 % Elapsed time: 0.186654 seconds
% 0.18/0.59 % CPU time: 1.173094 seconds
% 0.18/0.59 % Total memory used: 18.021 MB
% 0.18/0.59 % Net memory used: 16.670 MB
%------------------------------------------------------------------------------