%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 3.82s 1.04s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 7 RR)
% Number of literals : 24 ( 23 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t4,plain,
eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t21,plain,
eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = efalse,
inference(orient,[status(thm)],[t4]) ).
cnf(t3,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t6,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t3]) ).
cnf(t22,plain,
efalse = eq(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),apply(f(apply(apply(b,X1),X2)),apply(apply(apply(b,X1),X2),f(apply(apply(b,X1),X2))))),
inference(cp,[status(thm)],[t21,t6]) ).
cnf(t1456,plain,
efalse = eq(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2)))))),
inference(step,[status(thm)],[t22,t6]) ).
cnf(t1260,plain,
eq(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2)))))) = efalse,
inference(orient,[status(thm)],[t1456]) ).
cnf(t2,axiom,
apply(apply(l,X1),X2) = apply(X1,apply(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t10,plain,
apply(X1,apply(X2,X2)) = apply(apply(l,X1),X2),
inference(orient,[status(thm)],[t2]) ).
cnf(t1,axiom,
apply(m,X1) = apply(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,plain,
apply(X1,X1) = apply(m,X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t14,plain,
apply(apply(l,X1),X2) = apply(X1,apply(m,X2)),
inference(cp,[status(thm)],[t10,t5]) ).
cnf(t24,plain,
apply(apply(l,X1),X2) = apply(X1,apply(m,X2)),
inference(orient,[status(thm)],[t14]) ).
cnf(t25,plain,
apply(X1,apply(m,apply(l,X1))) = apply(m,apply(l,X1)),
inference(cp,[status(thm)],[t24,t5]) ).
cnf(t39,plain,
apply(X1,apply(m,apply(l,X1))) = apply(m,apply(l,X1)),
inference(orient,[status(thm)],[t25]) ).
cnf(t1328,plain,
efalse = eq(apply(m,apply(l,f(apply(apply(b,m),l)))),apply(m,apply(l,f(apply(apply(b,m),l))))),
inference(cp,[status(thm)],[t1260,t39]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t20,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t1457,plain,
efalse = etrue,
inference(step,[status(thm)],[t1328,t20]) ).
cnf(t1429,plain,
efalse = etrue,
inference(orient,[status(thm)],[t1457]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t1429]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.37 % Computer : n018.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Fri Sep 25 07:17:36 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.82/1.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.82/1.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------