%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 5.57s 6.35s
% Output : CNFRefutation 5.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 9 RR)
% Number of literals : 43 ( 42 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 68 ( 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(t13,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(w1,X1),X2) = apply(apply(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,plain,
apply(apply(X1,X2),X2) = apply(apply(w1,X2),X1),
inference(orient,[status(thm)],[t2]) ).
cnf(t6,plain,
apply(apply(w1,X1),apply(b,X2)) = apply(X2,apply(X1,X1)),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t67,plain,
apply(apply(w1,X1),apply(b,X2)) = apply(X2,apply(X1,X1)),
inference(orient,[status(thm)],[t6]) ).
cnf(t88,plain,
apply(X1,apply(apply(X2,X2),X3)) = apply(apply(apply(w1,X2),apply(b,apply(b,X1))),X3),
inference(cp,[status(thm)],[t4,t67]) ).
cnf(t11060,plain,
apply(X1,apply(apply(X2,X2),X3)) = apply(apply(apply(w1,X2),apply(b,apply(b,X1))),X3),
inference(orient,[status(thm)],[t88]) ).
cnf(t11141,plain,
efalse = eq(apply(apply(X1,X1),X2),apply(apply(apply(w1,X1),apply(b,apply(b,combinator))),X2)),
inference(cp,[status(thm)],[t13,t11060]) ).
cnf(t11637,plain,
eq(apply(apply(X1,X1),X2),apply(apply(apply(w1,X1),apply(b,apply(b,combinator))),X2)) = efalse,
inference(orient,[status(thm)],[t11141]) ).
cnf(t9,plain,
apply(apply(w1,X1),apply(X2,X1)) = apply(apply(apply(w1,X1),X2),X1),
inference(cp,[status(thm)],[t5,t5]) ).
cnf(t14,plain,
apply(apply(apply(w1,X1),X2),X1) = apply(apply(w1,X1),apply(X2,X1)),
inference(orient,[status(thm)],[t9]) ).
cnf(t11733,plain,
efalse = eq(apply(apply(X1,X1),X1),apply(apply(w1,X1),apply(apply(b,apply(b,combinator)),X1))),
inference(cp,[status(thm)],[t11637,t14]) ).
cnf(t11114,plain,
apply(apply(apply(w1,X1),apply(b,apply(b,X2))),X1) = apply(X2,apply(apply(w1,X1),X1)),
inference(cp,[status(thm)],[t11060,t5]) ).
cnf(t19586,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X1)) = apply(X2,apply(apply(w1,X1),X1)),
inference(step,[status(thm)],[t11114,t14]) ).
cnf(t11553,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X1)) = apply(X2,apply(apply(w1,X1),X1)),
inference(orient,[status(thm)],[t19586]) ).
cnf(t19589,plain,
efalse = eq(apply(apply(X1,X1),X1),apply(combinator,apply(apply(w1,X1),X1))),
inference(step,[status(thm)],[t11733,t11553]) ).
cnf(t11786,plain,
eq(apply(apply(X1,X1),X1),apply(combinator,apply(apply(w1,X1),X1))) = efalse,
inference(orient,[status(thm)],[t19589]) ).
cnf(t11817,plain,
efalse = eq(apply(apply(X1,X1),X1),apply(combinator,apply(apply(w1,X1),w1))),
inference(cp,[status(thm)],[t11786,t5]) ).
cnf(t12272,plain,
eq(apply(apply(X1,X1),X1),apply(combinator,apply(apply(w1,X1),w1))) = efalse,
inference(orient,[status(thm)],[t11817]) ).
cnf(t12278,plain,
efalse = eq(apply(apply(w1,X1),X1),apply(combinator,apply(apply(w1,X1),w1))),
inference(cp,[status(thm)],[t12272,t5]) ).
cnf(t12351,plain,
eq(apply(apply(w1,X1),X1),apply(combinator,apply(apply(w1,X1),w1))) = efalse,
inference(orient,[status(thm)],[t12278]) ).
cnf(t7,plain,
apply(apply(w1,X1),apply(apply(b,X2),X3)) = apply(apply(X2,apply(X3,X1)),X1),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t852,plain,
apply(apply(w1,X1),apply(apply(b,X2),X3)) = apply(apply(X2,apply(X3,X1)),X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t885,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(X3,X1),X1)),
inference(cp,[status(thm)],[t852,t4]) ).
cnf(t17886,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(X3,X1),X1)),
inference(orient,[status(thm)],[t885]) ).
cnf(t18048,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(w1,X1),X3)),
inference(cp,[status(thm)],[t17886,t5]) ).
cnf(t18615,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(w1,X1),X3)),
inference(orient,[status(thm)],[t18048]) ).
cnf(t18629,plain,
apply(X1,apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),X2)) = apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),w1),
inference(cp,[status(thm)],[t18615,t5]) ).
cnf(t19118,plain,
apply(X1,apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),X2)) = apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),w1),
inference(orient,[status(thm)],[t18629]) ).
cnf(t19267,plain,
efalse = eq(apply(apply(w1,apply(apply(b,apply(b,combinator)),w1)),apply(apply(b,apply(b,combinator)),w1)),apply(apply(w1,apply(apply(b,apply(b,combinator)),w1)),w1)),
inference(cp,[status(thm)],[t12351,t19118]) ).
cnf(t19623,plain,
efalse = eq(apply(combinator,apply(apply(w1,apply(apply(b,apply(b,combinator)),w1)),w1)),apply(apply(w1,apply(apply(b,apply(b,combinator)),w1)),w1)),
inference(step,[status(thm)],[t19267,t18615]) ).
cnf(t19624,plain,
efalse = eq(apply(apply(w1,apply(apply(b,apply(b,combinator)),w1)),w1),apply(apply(w1,apply(apply(b,apply(b,combinator)),w1)),w1)),
inference(step,[status(thm)],[t19623,t19118]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t12,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t19625,plain,
efalse = etrue,
inference(step,[status(thm)],[t19624,t12]) ).
cnf(t19437,plain,
efalse = etrue,
inference(orient,[status(thm)],[t19625]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t19437]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.37 % Computer : n017.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Fri Sep 25 07:10:08 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.57/6.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.57/6.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------