%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 : Tue Sep 29 09:37:08 AM UTC 2026
% Result : Unsatisfiable 85.80s 11.14s
% Output : CNFRefutation 86.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 2 RR)
% Number of literals : 42 ( 41 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(apply(Z,f(Z)),g(Z)) != apply(g(Z),apply(apply(f(Z),f(Z)),g(Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_combinator) ).
cnf(c2,axiom,
apply(apply(apply(s,X),Y),Z2) = apply(apply(X,Z2),apply(Y,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
cnf(c3,plain,
apply(apply(apply(s,s),apply(s,k)),X2) = apply(apply(s,X2),apply(apply(s,k),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X2),X3) = apply(apply(apply(s,X2),apply(apply(s,k),X2)),X3),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
apply(apply(apply(s,X3),apply(apply(s,k),X4)),X2) = apply(apply(X3,X2),apply(apply(apply(s,k),X4),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
apply(apply(apply(s,k),X2),X3) = apply(apply(k,X3),apply(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,axiom,
apply(apply(k,X2),Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
cnf(c8,plain,
apply(apply(k,X2),apply(X3,X2)) = X2,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(apply(s,k),X3),X2) = X2,
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
apply(apply(apply(s,k),X2),X3) = X3,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(apply(X4,X3),apply(apply(apply(s,k),X2),X3)) = apply(apply(X4,X3),X3),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
X2 = apply(apply(apply(s,k),X3),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c13,plain,
apply(apply(X4,X2),X2) = apply(apply(X4,X2),apply(apply(apply(s,k),X3),X2)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2) = apply(apply(X4,X2),apply(apply(apply(s,k),X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
apply(apply(X4,X2),apply(apply(apply(s,k),X3),X2)) = apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(apply(X4,X2),X2) = apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
apply(apply(X5,X3),apply(apply(apply(s,k),X2),X3)) = apply(apply(apply(s,X5),apply(apply(s,k),X4)),X3),
inference(transitivity,[status(thm)],[c11,c16]) ).
cnf(c18,plain,
apply(apply(apply(s,X5),apply(apply(s,k),X2)),X3) = apply(apply(apply(s,X5),apply(apply(s,k),X4)),X3),
inference(transitivity,[status(thm)],[c5,c17]) ).
cnf(c19,plain,
apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2) = apply(apply(apply(s,X4),apply(apply(s,k),X4)),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(apply(s,X4),apply(apply(s,k),X4)),X2) = apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X4),X2) = apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2),
inference(transitivity,[status(thm)],[c4,c20]) ).
cnf(c22,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))) = apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))) = apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2) = apply(apply(X4,X2),apply(apply(apply(s,k),X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
apply(apply(X4,X2),apply(apply(apply(s,k),X3),X2)) = apply(apply(X4,X2),X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c26,plain,
apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2) = apply(apply(X4,X2),X2),
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
apply(apply(apply(s,apply(s,apply(k,X4))),apply(apply(s,k),X2)),X3) = apply(apply(apply(s,apply(k,X4)),X3),X3),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(apply(apply(s,apply(k,X4)),X3),X2) = apply(apply(apply(k,X4),X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
apply(apply(k,X3),X2) = X3,
inference(substitution,[status(thm)],[c7]) ).
cnf(c30,plain,
apply(apply(apply(k,X4),X2),apply(X3,X2)) = apply(X4,apply(X3,X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
apply(apply(apply(s,apply(k,X4)),X3),X2) = apply(X4,apply(X3,X2)),
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
apply(apply(apply(s,apply(k,X3)),X2),X2) = apply(X3,apply(X2,X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
apply(apply(apply(s,apply(s,apply(k,X4))),apply(apply(s,k),X2)),X3) = apply(X4,apply(X3,X3)),
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))) = apply(apply(s,apply(apply(s,k),X3)),apply(f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3)))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3)))))))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))) = apply(apply(apply(s,apply(apply(s,k),X3)),apply(f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3)))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3)))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
apply(apply(apply(s,apply(apply(s,k),X4)),X3),X2) = apply(apply(apply(apply(s,k),X4),X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
apply(apply(apply(apply(s,k),X4),X2),apply(X3,X2)) = apply(X2,apply(X3,X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c38,plain,
apply(apply(apply(s,apply(apply(s,k),X4)),X3),X2) = apply(X2,apply(X3,X2)),
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
apply(apply(apply(s,apply(apply(s,k),X2)),apply(f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2))))))) = apply(g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))),apply(apply(f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))) = apply(g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3)))))),apply(apply(f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3)))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X3)))))))),
inference(transitivity,[status(thm)],[c35,c39]) ).
cnf(c41,plain,
apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2))))))) = apply(g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))),apply(apply(f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))),f(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2))))))),g(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(apply(s,k),X2)))))))),
inference(transitivity,[status(thm)],[c23,c40]) ).
cnf(c42,plain,
$false,
inference(resolution,[status(thm)],[c1,c41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n015.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:32:31 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 85.80/11.14 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 85.80/11.14
% 85.80/11.14 % SZS status Unsatisfiable
% 85.80/11.14
% 85.80/11.14 % SZS output start CNFRefutation
% See solution above
% 86.58/11.17
% 86.58/11.17 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------