%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL020-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 01:01:46 PM UTC 2026
% Result : Unsatisfiable 8.73s 6.63s
% Output : CNFRefutation 8.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 6 RR)
% Number of literals : 22 ( 21 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
Y != apply(combinator,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1,plain,
eq(X1,apply(combinator,X1)) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t22,plain,
eq(X1,apply(combinator,X1)) = efalse,
inference(orient,[status(thm)],[t1]) ).
cnf(t4,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(orient,[status(thm)],[t4]) ).
cnf(t3,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t6,plain,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t9,plain,
apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(cp,[status(thm)],[t7,t6]) ).
cnf(t65,plain,
apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(orient,[status(thm)],[t9]) ).
cnf(t2,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t2]) ).
cnf(t80,plain,
apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)),
inference(cp,[status(thm)],[t65,t5]) ).
cnf(t1404,plain,
apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)),
inference(orient,[status(thm)],[t80]) ).
cnf(t1558,plain,
efalse = eq(apply(apply(X1,X2),X2),apply(apply(apply(s,apply(c,apply(b,combinator))),X1),X2)),
inference(cp,[status(thm)],[t22,t1404]) ).
cnf(t1781,plain,
eq(apply(apply(X1,X2),X2),apply(apply(apply(s,apply(c,apply(b,combinator))),X1),X2)) = efalse,
inference(orient,[status(thm)],[t1558]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t21,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t1782,plain,
efalse = etrue,
inference(cp,[status(thm)],[t1781,t21]) ).
cnf(t1854,plain,
efalse = etrue,
inference(orient,[status(thm)],[t1782]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t1854]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL020-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n020.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 07:15:10 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.73/6.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.73/6.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------