%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL027-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 01:01:47 PM UTC 2026
% Result : Unsatisfiable 8.08s 1.64s
% Output : CNFRefutation 8.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 6 RR)
% Number of literals : 20 ( 19 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 : 33 ( 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(t15,plain,
eq(X1,apply(combinator,X1)) = efalse,
inference(orient,[status(thm)],[t1]) ).
cnf(t3,axiom,
apply(apply(apply(h,X1),X2),X3) = apply(apply(apply(X1,X2),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
apply(apply(apply(X1,X2),X3),X2) = apply(apply(apply(h,X1),X2),X3),
inference(orient,[status(thm)],[t3]) ).
cnf(t2,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t2]) ).
cnf(t7,plain,
apply(apply(apply(h,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X2),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t1275,plain,
apply(apply(apply(h,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t1329,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X2)),
inference(cp,[status(thm)],[t1275,t4]) ).
cnf(t11762,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X2)),
inference(orient,[status(thm)],[t1329]) ).
cnf(t12180,plain,
efalse = eq(apply(apply(X1,X2),X1),apply(apply(apply(h,apply(b,apply(b,combinator))),X1),X2)),
inference(cp,[status(thm)],[t15,t11762]) ).
cnf(t12326,plain,
eq(apply(apply(X1,X2),X1),apply(apply(apply(h,apply(b,apply(b,combinator))),X1),X2)) = efalse,
inference(orient,[status(thm)],[t12180]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t14,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t12327,plain,
efalse = etrue,
inference(cp,[status(thm)],[t12326,t14]) ).
cnf(t13140,plain,
efalse = etrue,
inference(orient,[status(thm)],[t12327]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t13140]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL027-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Fri Sep 25 07:14:44 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.08/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.08/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------