%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 16.29s 13.74s
% Output : CNFRefutation 16.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 9 RR)
% Number of literals : 36 ( 35 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
Y != apply(combinator,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1,plain,
eq(X1,apply(combinator,X1)) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t14,plain,
eq(X1,apply(combinator,X1)) = efalse,
inference(orient,[status(thm)],[t1]) ).
cnf(t3,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t4,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t3]) ).
cnf(t2,axiom,
apply(apply(l2,X1),X2) = apply(X2,apply(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,plain,
apply(X1,apply(X2,X2)) = apply(apply(l2,X2),X1),
inference(orient,[status(thm)],[t2]) ).
cnf(t8,plain,
apply(X1,apply(apply(X2,X2),X3)) = apply(apply(apply(l2,X2),apply(b,X1)),X3),
inference(cp,[status(thm)],[t4,t5]) ).
cnf(t980,plain,
apply(X1,apply(apply(X2,X2),X3)) = apply(apply(apply(l2,X2),apply(b,X1)),X3),
inference(orient,[status(thm)],[t8]) ).
cnf(t1026,plain,
efalse = eq(apply(apply(X1,X1),X2),apply(apply(apply(l2,X1),apply(b,combinator)),X2)),
inference(cp,[status(thm)],[t14,t980]) ).
cnf(t1359,plain,
eq(apply(apply(X1,X1),X2),apply(apply(apply(l2,X1),apply(b,combinator)),X2)) = efalse,
inference(orient,[status(thm)],[t1026]) ).
cnf(t1404,plain,
efalse = eq(apply(apply(X1,X1),apply(X2,X2)),apply(apply(l2,X2),apply(apply(l2,X1),apply(b,combinator)))),
inference(cp,[status(thm)],[t1359,t5]) ).
cnf(t11,plain,
apply(apply(l2,X1),apply(l2,X2)) = apply(apply(X1,X1),apply(X2,X2)),
inference(cp,[status(thm)],[t5,t5]) ).
cnf(t123,plain,
apply(apply(l2,X1),apply(l2,X2)) = apply(apply(X1,X1),apply(X2,X2)),
inference(orient,[status(thm)],[t11]) ).
cnf(t1000,plain,
apply(apply(apply(l2,X1),apply(b,X2)),apply(X3,X3)) = apply(X2,apply(apply(l2,X1),apply(l2,X3))),
inference(cp,[status(thm)],[t980,t123]) ).
cnf(t1170,plain,
apply(apply(apply(l2,X1),apply(b,X2)),apply(X3,X3)) = apply(X2,apply(apply(l2,X1),apply(l2,X3))),
inference(orient,[status(thm)],[t1000]) ).
cnf(t1174,plain,
apply(X1,apply(apply(l2,X2),apply(l2,X3))) = apply(apply(l2,X3),apply(apply(l2,X2),apply(b,X1))),
inference(cp,[status(thm)],[t1170,t5]) ).
cnf(t1247,plain,
apply(apply(l2,X1),apply(apply(l2,X2),apply(b,X3))) = apply(X3,apply(apply(l2,X2),apply(l2,X1))),
inference(orient,[status(thm)],[t1174]) ).
cnf(t25078,plain,
efalse = eq(apply(apply(X1,X1),apply(X2,X2)),apply(combinator,apply(apply(l2,X1),apply(l2,X2)))),
inference(step,[status(thm)],[t1404,t1247]) ).
cnf(t2746,plain,
eq(apply(apply(X1,X1),apply(X2,X2)),apply(combinator,apply(apply(l2,X1),apply(l2,X2)))) = efalse,
inference(orient,[status(thm)],[t25078]) ).
cnf(t145,plain,
apply(apply(l2,apply(apply(b,X1),X2)),apply(l2,X3)) = apply(apply(X1,apply(X2,apply(apply(b,X1),X2))),apply(X3,X3)),
inference(cp,[status(thm)],[t123,t4]) ).
cnf(t3475,plain,
apply(apply(X1,apply(X2,apply(apply(b,X1),X2))),apply(X3,X3)) = apply(apply(l2,apply(apply(b,X1),X2)),apply(l2,X3)),
inference(orient,[status(thm)],[t145]) ).
cnf(t3481,plain,
apply(apply(l2,apply(apply(b,apply(b,X1)),X2)),apply(l2,X3)) = apply(X1,apply(apply(X2,apply(apply(b,apply(b,X1)),X2)),apply(X3,X3))),
inference(cp,[status(thm)],[t3475,t4]) ).
cnf(t24527,plain,
apply(X1,apply(apply(X2,apply(apply(b,apply(b,X1)),X2)),apply(X3,X3))) = apply(apply(l2,apply(apply(b,apply(b,X1)),X2)),apply(l2,X3)),
inference(orient,[status(thm)],[t3481]) ).
cnf(t24849,plain,
efalse = eq(apply(apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)),apply(l2,l2)),apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(l2,l2))),
inference(cp,[status(thm)],[t2746,t24527]) ).
cnf(t125,plain,
apply(apply(X1,X1),apply(l2,l2)) = apply(apply(l2,l2),apply(l2,X1)),
inference(cp,[status(thm)],[t123,t5]) ).
cnf(t165,plain,
apply(apply(X1,X1),apply(l2,l2)) = apply(apply(l2,l2),apply(l2,X1)),
inference(orient,[status(thm)],[t125]) ).
cnf(t25158,plain,
efalse = eq(apply(apply(l2,l2),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(l2,l2))),
inference(step,[status(thm)],[t24849,t165]) ).
cnf(t25159,plain,
efalse = eq(apply(apply(l2,l2),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(l2,l2),apply(l2,apply(apply(b,apply(b,combinator)),l2)))),
inference(step,[status(thm)],[t25158,t5]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t13,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t25160,plain,
efalse = etrue,
inference(step,[status(thm)],[t25159,t13]) ).
cnf(t25002,plain,
efalse = etrue,
inference(orient,[status(thm)],[t25160]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t25002]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/11.63 % Computer : n013.cluster.edu
% 0.11/11.63 % Model : x86_64 x86_64
% 0.11/11.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/11.63 % Memory : 8046.5625MB
% 0.11/11.63 % OS : Linux 6.8.0-71-generic
% 0.11/11.63 % CPULimit : 300
% 0.11/11.63 % WCLimit : 300
% 0.11/11.63 % DateTime : Fri Sep 25 07:10:51 UTC 2026
% 0.11/11.63 % CPUTime :
% 0.11/11.63 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.29/13.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.29/13.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------