%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL002-4 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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 : n016.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 1.32s 1.74s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 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,
weak_fixed_point(X1) = apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
cnf(prove_weak_fixed_point,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
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,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_10,plain,
apply(apply(apply(s,i),i),X1) = apply(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_11,axiom,
weak_fixed_point(X1) = apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)),
weak_fixed_point ).
cnf(c_0_12,plain,
apply(apply(apply(s,apply(b,X1)),i),X2) = apply(X1,apply(apply(apply(s,i),i),X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
apply(apply(apply(s,i),i),apply(apply(s,apply(b,X1)),i)) = weak_fixed_point(X1),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
prove_weak_fixed_point ).
cnf(c_0_15,plain,
apply(X1,weak_fixed_point(X1)) = weak_fixed_point(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_12]),c_0_13]),c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL002-4 : TPTP v9.2.1. Bugfixed v3.1.0.
% 0.00/0.12 % 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
% 0.14/0.32 % Computer : n016.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 16:14:36 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.32/1.74 % Version : CSE_E---1.7
% 1.32/1.74 % Problem : theBenchmark.p
% 1.32/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.32/1.74 % SZS output start CNFRefutation
% See solution above
% 1.32/1.74 % Total time : 1.374s
%------------------------------------------------------------------------------