%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO002-4 : TPTP v9.2.1. Released v1.1.0.
% 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 : n018.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 04:18:56 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 38 ( 14 unt; 0 nHn; 24 RR)
% Number of literals : 81 ( 0 equ; 45 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 144 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_betweeness,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
cnf(between_substitution3,axiom,
( between(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ between(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_substitution3) ).
cnf(identity_for_equidistance,axiom,
( equalish(X1,X2)
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
cnf(outer_pasch2,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch2) ).
cnf(outer_pasch1,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch1) ).
cnf(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
cnf(c_0_8,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
transitivity_for_betweeness ).
cnf(c_0_9,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_10,plain,
( between(X1,X2,X3)
| ~ between(X1,X2,extension(X2,X3,X4,X5)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
( between(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ between(X3,X4,X1) ),
between_substitution3 ).
cnf(c_0_12,plain,
between(X1,X1,X1),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_13,axiom,
( equalish(X1,X2)
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_14,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_15,plain,
( between(X1,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
equalish(X1,extension(X2,X1,X3,X3)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
between(X1,X1,extension(X2,X1,X3,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
( between(X1,X2,X2)
| ~ between(X1,X2,extension(X3,X2,X4,X4)) ),
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
cnf(c_0_19,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_20,plain,
( between(X1,X2,X3)
| ~ equalish(X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_21,plain,
between(X1,X2,extension(X3,X2,X4,X4)),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_22,plain,
( between(X1,X2,X3)
| ~ between(X1,X2,extension(X4,X3,X5,X5)) ),
inference(spm,[status(thm)],[c_0_8,c_0_21]) ).
cnf(c_0_23,plain,
between(X1,extension(X2,X3,X4,X4),X3),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_24,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch2 ).
cnf(c_0_25,plain,
( between(X1,X2,extension(X3,X4,X5,X5))
| ~ between(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_8,c_0_23]) ).
cnf(c_0_26,plain,
( between(X1,X2,X3)
| ~ equalish(outer_pasch(X2,X4,X5,X1,X6),X3)
| ~ between(X5,X6,X1)
| ~ between(X4,X2,X6) ),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_27,plain,
( between(X1,X2,X3)
| ~ between(X1,X2,extension(X4,X5,X6,X6))
| ~ between(X2,X3,X5) ),
inference(spm,[status(thm)],[c_0_8,c_0_25]) ).
cnf(c_0_28,plain,
( between(X1,X2,extension(X3,outer_pasch(X2,X4,X5,X1,X6),X7,X7))
| ~ between(X5,X6,X1)
| ~ between(X4,X2,X6) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_29,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch1 ).
cnf(c_0_30,plain,
( between(X1,X2,X3)
| ~ between(X2,X3,outer_pasch(X2,X4,X5,X1,X6))
| ~ between(X5,X6,X1)
| ~ between(X4,X2,X6) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( between(X1,X2,outer_pasch(X3,X2,X4,X5,X6))
| ~ between(X1,X2,X4)
| ~ between(X4,X6,X5)
| ~ between(X2,X3,X6) ),
inference(spm,[status(thm)],[c_0_8,c_0_29]) ).
cnf(c_0_32,plain,
( between(X1,X2,X3)
| ~ between(X4,X5,X1)
| ~ between(X3,X2,X5)
| ~ between(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
( between(X1,X2,X3)
| ~ between(X3,X2,X1)
| ~ between(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_34,plain,
( between(X1,X1,X2)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_35,negated_conjecture,
~ between(a,a,b),
prove_a_between_a_and_b ).
cnf(c_0_36,plain,
between(X1,X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_9]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO002-4 : TPTP v9.2.1. Released v1.1.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n018.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 17:36:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------