%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:01:40 PM UTC 2026
% Result : Unsatisfiable 0.14s 11.02s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 12 RR)
% Number of literals : 16 ( 15 equ; 11 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t15,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(orient,[status(thm)],[t1]) ).
cnf(t0,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
apply(apply(k,X1),X2) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[goal_0,t15]) ).
cnf(g0_1,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_0,t14]) ).
cnf(g0_2,plain,
apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_1,t15]) ).
cnf(g0_3,plain,
apply(apply(apply(k,y),apply(k,y)),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_2,t15]) ).
cnf(g0_4,plain,
apply(y,apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_3,t14]) ).
cnf(g0_5,plain,
apply(y,apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_4,t15]) ).
cnf(g0_6,plain,
apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_5,t15]) ).
cnf(g0_7,plain,
apply(y,apply(apply(x,apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_6,t14]) ).
cnf(g0_8,plain,
apply(y,apply(apply(x,apply(apply(k,x),apply(k,x))),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_7,t15]) ).
cnf(g0_9,plain,
apply(y,apply(apply(x,x),y)) != apply(y,apply(apply(x,x),y)),
inference(rw,[status(thm)],[g0_8,t14]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.37 % Computer : n004.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Fri Sep 25 07:09:46 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/11.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/11.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------