%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO008-1 : TPTP v9.2.1. Bugfixed v2.5.0.
% 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 : 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 04:18:57 PM UTC 2026
% Result : Unsatisfiable 2.20s 1.96s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 16 unt; 0 nHn; 26 RR)
% Number of literals : 59 ( 6 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-5 aty)
% Number of variables : 76 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
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/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
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/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
cnf(d_between_a_and_e,hypothesis,
between(a,d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_between_a_and_e) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
cnf(b_between_c_and_d,hypothesis,
between(c,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_between_c_and_d) ).
cnf(c_between_a_and_e,hypothesis,
between(a,c,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_e) ).
cnf(prove_betweenness,negated_conjecture,
~ between(a,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_betweenness) ).
cnf(c_0_10,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_11,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch1 ).
cnf(c_0_12,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch2 ).
cnf(c_0_13,plain,
( outer_pasch(X1,X2,X2,X3,X4) = X2
| ~ between(X2,X4,X3)
| ~ between(X2,X1,X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_15,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_16,plain,
( between(X1,X2,X3)
| ~ between(X3,X4,X1)
| ~ between(X3,X2,X4) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,hypothesis,
between(a,d,e),
d_between_a_and_e ).
cnf(c_0_18,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_19,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
( between(e,X1,a)
| ~ between(a,X1,d) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,hypothesis,
( between(a,X1,e)
| ~ between(a,X2,d)
| ~ between(e,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_23,plain,
( between(X1,X2,X3)
| ~ between(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_24,hypothesis,
( between(a,X1,e)
| ~ between(a,outer_pasch(X1,X2,X3,e,X4),d)
| ~ between(X3,X4,e)
| ~ between(X2,X1,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_25,plain,
( between(X1,outer_pasch(X2,X3,X1,X4,X5),X3)
| ~ between(X1,X5,X4)
| ~ between(X3,X2,X5) ),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_26,hypothesis,
between(c,b,d),
b_between_c_and_d ).
cnf(c_0_27,hypothesis,
( between(a,X1,e)
| ~ between(a,X2,e)
| ~ between(d,X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,hypothesis,
between(d,b,c),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_29,hypothesis,
between(a,c,e),
c_between_a_and_e ).
cnf(c_0_30,negated_conjecture,
~ between(a,b,e),
prove_betweenness ).
cnf(c_0_31,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO008-1 : TPTP v9.2.1. Bugfixed v2.5.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:36:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.20/1.96 % Version : CSE_E---1.7
% 2.20/1.96 % Problem : theBenchmark.p
% 2.20/1.96 % SZS status Unsatisfiable for theBenchmark.p
% 2.20/1.96 % SZS output start CNFRefutation
% See solution above
% 2.20/1.96 % Total time : 1.368s
%------------------------------------------------------------------------------