%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO006-1 : 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 : n025.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 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 18 unt; 3 nHn; 30 RR)
% Number of literals : 61 ( 14 equ; 27 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 67 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_betweeness,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
cnf(c_between_a_and_d,hypothesis,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
cnf(prove_not_between_others,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
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(a_not_c,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
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(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
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(c_not_d,hypothesis,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
cnf(c_0_11,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
transitivity_for_betweeness ).
cnf(c_0_12,hypothesis,
between(a,c,d),
c_between_a_and_d ).
cnf(c_0_13,hypothesis,
( between(X1,a,c)
| ~ between(X1,a,d) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
prove_not_between_others ).
cnf(c_0_15,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_16,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch1 ).
cnf(c_0_17,negated_conjecture,
( between(a,d,c)
| between(c,a,c) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
a != c,
a_not_c ).
cnf(c_0_19,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_20,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_21,plain,
( outer_pasch(X1,X2,X2,X3,X4) = X2
| ~ between(X2,X4,X3)
| ~ between(X2,X1,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
between(a,d,c),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_17]),c_0_18]) ).
cnf(c_0_23,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_24,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( outer_pasch(X1,a,a,c,d) = a
| ~ between(a,X1,d) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch2 ).
cnf(c_0_28,negated_conjecture,
outer_pasch(d,a,a,c,d) = a,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
between(c,d,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22]),c_0_26])]) ).
cnf(c_0_30,hypothesis,
( outer_pasch(X1,a,a,d,c) = a
| ~ between(a,X1,c) ),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_31,negated_conjecture,
( between(X1,c,d)
| ~ between(X1,c,a) ),
inference(spm,[status(thm)],[c_0_11,c_0_29]) ).
cnf(c_0_32,hypothesis,
c != d,
c_not_d ).
cnf(c_0_33,hypothesis,
outer_pasch(c,a,a,d,c) = a,
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ between(d,c,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_31]),c_0_32]) ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_33]),c_0_12]),c_0_26])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO006-1 : 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
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:36:13 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------