%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL021-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.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 04:12:03 PM UTC 2026
% Result : Unsatisfiable 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of clauses : 34 ( 26 unt; 0 nHn; 14 RR)
% Number of literals : 44 ( 43 equ; 19 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(v_definition,axiom,
apply(apply(apply(v,X1),X2),X3) = apply(apply(X3,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(m_definition,axiom,
apply(m,X1) = apply(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_definition) ).
cnf(prove_fixed_point,negated_conjecture,
X1 != apply(combinator,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(i_0_4,axiom,
apply(apply(apply(v,X1),X2),X3) = apply(apply(X3,X1),X2),
v_definition,
[final] ).
cnf(i_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition,
[final] ).
cnf(i_0_6,axiom,
apply(m,X1) = apply(X1,X1),
m_definition,
[final] ).
cnf(i_0_7,negated_conjecture,
X1 != apply(combinator,X1),
prove_fixed_point,
[final] ).
cnf(i_0_8,axiom,
X1 = X1 ).
cnf(i_0_9,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_10,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_11,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_12,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_8_001,axiom,
X1 = X1 ).
cnf(i_0_9_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_10_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_11_004,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_12_005,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_13,plain,
apply(X1,X1) = apply(m,X1),
inference(scs_inference,[],[i_0_6,i_0_9]) ).
cnf(i_0_14,plain,
combinator != apply(m,combinator),
inference(scs_inference,[],[i_0_7,i_0_6,i_0_9,i_0_10]) ).
cnf(i_0_15,plain,
apply(m,X1) = apply(X1,X1),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_16,plain,
X1 != apply(combinator,X1),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_17,plain,
apply(apply(X1,X2),X3) = apply(apply(apply(v,X2),X3),X1),
inference(scs_inference,[],[i_0_4,i_0_9]) ).
cnf(i_0_18,plain,
apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3),
inference(scs_inference,[],[i_0_5,i_0_9]) ).
cnf(i_0_19,plain,
apply(X1,apply(X2,X3)) = apply(apply(apply(v,X2),X3),apply(b,X1)),
inference(scs_inference,[],[i_0_17,i_0_18,i_0_10]) ).
cnf(i_0_20,plain,
apply(apply(X1,X2),X3) = apply(apply(apply(v,X2),X3),X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_21,plain,
apply(apply(apply(v,X1),X2),apply(b,X3)) = apply(X3,apply(X1,X2)),
inference(scs_inference,[],[i_0_17,i_0_18,i_0_10,i_0_9]) ).
cnf(i_0_22,plain,
apply(X1,X2) != apply(apply(apply(v,X1),X2),apply(b,combinator)),
inference(scs_inference,[],[i_0_7,i_0_21,i_0_10]) ).
cnf(i_0_23,plain,
apply(apply(apply(v,X1),X2),apply(b,X3)) = apply(X3,apply(X1,X2)),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_24,plain,
X1 != apply(combinator,X1),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_25,plain,
X1 != apply(apply(v,X1),apply(b,combinator)),
inference(scs_inference,[],[i_0_7,i_0_21,i_0_10,i_0_11]) ).
cnf(i_0_26,plain,
X1 != apply(v,apply(X1,apply(b,combinator))),
inference(scs_inference,[],[i_0_25,i_0_11]) ).
cnf(i_0_27,plain,
X1 != apply(apply(v,X1),apply(b,combinator)),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_28,plain,
$false,
inference(scs_inference,[],[i_0_17,i_0_25,i_0_22,i_0_6,i_0_11,i_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL021-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n023.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 16:15:08 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.64 % Total time : 1.269s
%------------------------------------------------------------------------------