%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 13.81s 2.19s
% Output : CNFRefutation 13.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 25 RR)
% Number of literals : 33 ( 32 equ; 22 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 : 20 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)) = strong_fixed_point,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)) = strong_fixed_point,
inference(orient,[status(thm)],[t2]) ).
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(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(t6,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(cp,[status(thm)],[t4,t3]) ).
cnf(t26,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t6]) ).
cnf(t5,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(cp,[status(thm)],[t4,t3]) ).
cnf(t17,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(orient,[status(thm)],[t5]) ).
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(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),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,s),apply(s,k))),apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k)))))),apply(apply(s,apply(k,s)),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(s,apply(apply(s,s),apply(s,k))),apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k)))),apply(apply(apply(s,apply(k,s)),k),fixed_pt))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_1,t26]) ).
cnf(g0_3,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k)))),apply(s,apply(k,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_2,t26]) ).
cnf(g0_4,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(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(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),fixed_pt),
inference(rw,[status(thm)],[g0_4,t13]) ).
cnf(g0_6,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k)))))),apply(apply(s,apply(k,s)),k)),fixed_pt),
inference(rw,[status(thm)],[g0_5,t4]) ).
cnf(g0_7,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k))))))),apply(apply(s,apply(k,s)),k)),fixed_pt),
inference(rw,[status(thm)],[g0_6,t4]) ).
cnf(g0_8,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))))),fixed_pt),apply(apply(apply(s,apply(k,s)),k),fixed_pt)),
inference(rw,[status(thm)],[g0_7,t4]) ).
cnf(g0_9,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))))),fixed_pt),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),
inference(rw,[status(thm)],[g0_8,t4]) ).
cnf(g0_10,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k))))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),
inference(rw,[status(thm)],[g0_9,t3]) ).
cnf(g0_11,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))),
inference(rw,[status(thm)],[g0_10,t4]) ).
cnf(g0_12,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(s,k),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))),
inference(rw,[status(thm)],[g0_11,t4]) ).
cnf(g0_13,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))),apply(apply(apply(s,k),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))))),
inference(rw,[status(thm)],[g0_12,t4]) ).
cnf(g0_14,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))),apply(apply(apply(s,k),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))))),
inference(rw,[status(thm)],[g0_13,t4]) ).
cnf(g0_15,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))),apply(apply(apply(s,k),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[g0_14,t3]) ).
cnf(g0_16,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),apply(k,apply(apply(s,s),apply(s,k)))),apply(s,apply(k,fixed_pt)))),apply(apply(apply(s,k),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[g0_15,t3]) ).
cnf(g0_17,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),apply(apply(apply(s,k),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[g0_16,t3]) ).
cnf(g0_18,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),apply(apply(apply(s,k),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[g0_17,t3]) ).
cnf(g0_19,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))),
inference(rw,[status(thm)],[g0_18,t17]) ).
cnf(g0_20,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))) != apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(apply(s,k),k),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))))),
inference(rw,[status(thm)],[g0_19,t26]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 07:09:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.81/2.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.81/2.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------