%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 : Fri Sep 25 01:51:36 PM UTC 2026
% Result : Theorem 6.00s 1.18s
% Output : Proof 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 72 unt; 0 def)
% Number of atoms : 86 ( 74 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 6 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 103 ( 10 sgn 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain5) ).
fof(f20_nnf,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c21,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t15,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t73,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t15]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t20,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f16,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f16_nnf,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c17,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi17,axiom,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t14,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi17]) ).
cnf(t92,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(orient,[status(thm)],[t14]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t32,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t93,plain,
true = leq(one,domain(one)),
inference(cp,[status(thm)],[t92,t32]) ).
cnf(t172,plain,
leq(one,domain(one)) = true,
inference(orient,[status(thm)],[t93]) ).
cnf(t173,plain,
domain(one) = ifeq(true,true,addition(one,domain(one)),domain(one)),
inference(cp,[status(thm)],[t35,t172]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t199,plain,
domain(one) = addition(one,domain(one)),
inference(step,[status(thm)],[t173,t34]) ).
fof(f18,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f18_nnf,plain,
! [X0] : addition(domain(X0),one) = one,
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X0] : addition(domain(X0),one) = one,
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c19,plain,
addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t10,plain,
addition(domain(X1),one) = one,
inference(equality_encoding,[status(esa)],[c19]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f0_nnf,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t12,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t38,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t196,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t10,t38]) ).
cnf(t77,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t196]) ).
cnf(t200,plain,
domain(one) = one,
inference(step,[status(thm)],[t199,t77]) ).
cnf(t175,plain,
domain(one) = one,
inference(orient,[status(thm)],[t200]) ).
cnf(t176,plain,
domain(addition(one,X1)) = addition(one,domain(X1)),
inference(cp,[status(thm)],[t73,t175]) ).
cnf(t202,plain,
domain(addition(one,X1)) = one,
inference(step,[status(thm)],[t176,t77]) ).
cnf(t181,plain,
domain(addition(one,X1)) = one,
inference(orient,[status(thm)],[t202]) ).
cnf(hi11,axiom,
ifeq(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
fof(f12,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f12_nnf,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi13,axiom,
leq(addition(one,multiplication(X0,star(X0))),star(X0)) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t24,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi13]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t18,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t41,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t192,plain,
addition(one,addition(multiplication(X1,star(X1)),star(X1))) = star(X1),
inference(step,[status(thm)],[t24,t41]) ).
cnf(t193,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(step,[status(thm)],[t192,t38]) ).
cnf(t53,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(orient,[status(thm)],[t193]) ).
cnf(t182,plain,
one = domain(star(X1)),
inference(cp,[status(thm)],[t181,t53]) ).
cnf(t188,plain,
domain(star(X1)) = one,
inference(orient,[status(thm)],[t182]) ).
fof(f21,conjecture,
! [X0] : domain(star(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f21_neg,negated_conjecture,
~ ! [X0] : domain(star(X0)) = one,
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [X0] : domain(star(X0)) != one,
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
domain(star(sk0)) != one,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f21_nnf]) ).
cnf(c22,plain,
domain(star(sk0)) != one,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
domain(star(sk0)) != one,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
one != one,
inference(rw,[status(thm)],[goal_0,t188]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 18:55:38 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.00/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.00/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------