%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL002-1 : 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 : n022.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 0.31s 1.61s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of clauses : 31 ( 23 unt; 0 nHn; 12 RR)
% Number of literals : 41 ( 40 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 63 ( 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(c_definition,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_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(prove_fixed_point,negated_conjecture,
X1 != apply(fixed_pt,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(i_definition,axiom,
apply(i,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
cnf(i_0_5,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition,
[final] ).
cnf(i_0_6,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
c_definition,
[final] ).
cnf(i_0_7,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition,
[final] ).
cnf(i_0_8,negated_conjecture,
X1 != apply(fixed_pt,X1),
prove_fixed_point,
[final] ).
cnf(i_0_9,axiom,
apply(i,X1) = X1,
i_definition,
[final] ).
cnf(i_0_10,axiom,
X1 = X1 ).
cnf(i_0_11,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_12,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_13,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_14,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_10_001,axiom,
X1 = X1 ).
cnf(i_0_11_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_12_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_13_004,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_14_005,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_15,plain,
X1 = apply(i,X1),
inference(scs_inference,[],[i_0_9,i_0_11]) ).
cnf(i_0_16,plain,
X1 != apply(i,apply(fixed_pt,X1)),
inference(scs_inference,[],[i_0_8,i_0_9,i_0_11,i_0_12]) ).
cnf(i_0_17,plain,
apply(i,X1) = X1,
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_18,plain,
X1 != apply(fixed_pt,apply(i,X1)),
inference(scs_inference,[],[i_0_8,i_0_9,i_0_11,i_0_12,i_0_14]) ).
cnf(i_0_19,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(scs_inference,[],[i_0_5,i_0_11]) ).
cnf(i_0_20,plain,
apply(X1,X2) != apply(apply(apply(b,fixed_pt),X1),X2),
inference(scs_inference,[],[i_0_8,i_0_5,i_0_7,i_0_11,i_0_12]) ).
cnf(i_0_21,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_22,plain,
X1 != apply(fixed_pt,X1),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_23,plain,
X1 != apply(apply(b,fixed_pt),X1),
inference(scs_inference,[],[i_0_8,i_0_5,i_0_7,i_0_11,i_0_12,i_0_13]) ).
cnf(i_0_24,plain,
apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2),
inference(scs_inference,[],[i_0_6,i_0_11]) ).
cnf(i_0_25,plain,
$false,
inference(scs_inference,[],[i_0_20,i_0_6,i_0_5,i_0_11,i_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL002-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n022.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 16:17:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.31/1.61 % Version : CSE_E---1.7
% 0.31/1.61 % Problem : theBenchmark.p
% 0.31/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.31/1.61 % SZS output start CNFRefutation
% See solution above
% 0.31/1.64 % Total time : 1.270s
%------------------------------------------------------------------------------