%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:01:44 PM UTC 2026
% Result : Unsatisfiable 4.68s 1.12s
% Output : CNFRefutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 28 RR)
% Number of literals : 32 ( 31 equ; 24 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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(t2,axiom,
apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) = strong_fixed_point,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(t4,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(orient,[status(thm)],[t1]) ).
cnf(t16,plain,
apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) = strong_fixed_point,
inference(step,[status(thm)],[t2,t4]) ).
cnf(t13,plain,
apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) = strong_fixed_point,
inference(orient,[status(thm)],[t16]) ).
cnf(t0,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t3,plain,
apply(apply(k,X1),X2) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(g0_1,plain,
apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_0,t4]) ).
cnf(g0_2,plain,
apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_1,t4]) ).
cnf(g0_3,plain,
apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_2,t4]) ).
cnf(g0_4,plain,
apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_3,t4]) ).
cnf(g0_5,plain,
apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_4,t3]) ).
cnf(g0_6,plain,
apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_5,t3]) ).
cnf(g0_7,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_6,t3]) ).
cnf(g0_8,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt),
inference(rw,[status(thm)],[g0_7,t13]) ).
cnf(g0_9,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt),
inference(rw,[status(thm)],[g0_8,t4]) ).
cnf(g0_10,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)),
inference(rw,[status(thm)],[g0_9,t4]) ).
cnf(g0_11,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt))),
inference(rw,[status(thm)],[g0_10,t4]) ).
cnf(g0_12,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt))),
inference(rw,[status(thm)],[g0_11,t4]) ).
cnf(g0_13,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(rw,[status(thm)],[g0_12,t3]) ).
cnf(g0_14,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(rw,[status(thm)],[g0_13,t3]) ).
cnf(g0_15,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(rw,[status(thm)],[g0_14,t3]) ).
cnf(g0_16,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(rw,[status(thm)],[g0_15,t4]) ).
cnf(g0_17,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
inference(rw,[status(thm)],[g0_16,t4]) ).
cnf(g0_18,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),apply(apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
inference(rw,[status(thm)],[g0_17,t4]) ).
cnf(g0_19,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(k,apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(rw,[status(thm)],[g0_18,t3]) ).
cnf(g0_20,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(rw,[status(thm)],[g0_19,t3]) ).
cnf(g0_21,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(k,fixed_pt),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(rw,[status(thm)],[g0_20,t4]) ).
cnf(g0_22,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(rw,[status(thm)],[g0_21,t3]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:11:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.68/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.68/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------