%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL002-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:11:58 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.75s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 13 unt; 0 nHn; 8 RR)
% Number of literals : 21 ( 13 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
cnf(i_definition,axiom,
apply(i,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(weak_fixed_point,axiom,
( fixed_point(X1)
| X1 != apply(fixed_pt,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
cnf(prove_weak_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
cnf(c_0_5,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_6,axiom,
apply(i,X1) = X1,
i_definition ).
cnf(c_0_7,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_8,plain,
apply(apply(apply(s,X1),i),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,axiom,
( fixed_point(X1)
| X1 != apply(fixed_pt,X1) ),
weak_fixed_point ).
cnf(c_0_10,plain,
apply(apply(apply(s,apply(b,X1)),i),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( fixed_point(apply(X1,X1))
| apply(apply(apply(s,apply(b,fixed_pt)),i),X1) != apply(X1,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
apply(apply(apply(s,i),i),X1) = apply(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_13,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),
prove_weak_fixed_point ).
cnf(c_0_14,plain,
( fixed_point(apply(apply(apply(s,i),i),X1))
| apply(apply(apply(s,apply(b,fixed_pt)),i),X1) != apply(apply(apply(s,i),i),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
~ fixed_point(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X1)),i))),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_16,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COL002-2 : TPTP v9.2.1. Released v1.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 16:18:28 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.20/0.35 % start to proof: theBenchmark
% 1.33/1.75 % Version : CSE_E---1.7
% 1.33/1.75 % Problem : theBenchmark.p
% 1.33/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.75 % SZS output start CNFRefutation
% See solution above
% 1.33/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------