%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO007-1 : TPTP v9.2.1. Bugfixed v2.5.0.
% 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 : n028.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 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 48 ( 27 unt; 6 nHn; 42 RR)
% Number of literals : 83 ( 19 equ; 36 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 77 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
cnf(a_between_a_and_e,hypothesis,
between(e,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_between_a_and_e) ).
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/Axioms/GEO001-0.ax',outer_pasch2) ).
cnf(a_between_a_and_c,hypothesis,
between(d,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_between_a_and_c) ).
cnf(connectivity_for_betweeness,axiom,
( X1 = X2
| between(X1,X3,X4)
| between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',connectivity_for_betweeness) ).
cnf(a_not_c,hypothesis,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
cnf(transitivity_for_betweeness,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
cnf(e_not_between_d_and_a,hypothesis,
~ between(d,e,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_not_between_d_and_a) ).
cnf(prove_d_between_e_and_a,negated_conjecture,
~ between(e,d,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_between_e_and_a) ).
cnf(c_0_13,axiom,
( 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,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,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_18,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,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_20,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( outer_pasch(X1,X2,X2,X3,X3) = X2
| ~ between(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,hypothesis,
between(e,a,c),
a_between_a_and_e ).
cnf(c_0_23,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch2 ).
cnf(c_0_24,hypothesis,
outer_pasch(a,e,e,c,c) = e,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
between(d,a,c),
a_between_a_and_c ).
cnf(c_0_26,axiom,
( X1 = X2
| between(X1,X3,X4)
| between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
connectivity_for_betweeness ).
cnf(c_0_27,hypothesis,
between(c,a,e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]),c_0_22])]) ).
cnf(c_0_28,hypothesis,
a != c,
a_not_c ).
cnf(c_0_29,hypothesis,
outer_pasch(a,d,d,c,c) = d,
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_30,hypothesis,
( between(c,X1,e)
| between(c,e,X1)
| ~ between(c,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_31,hypothesis,
between(c,a,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_20]),c_0_25])]) ).
cnf(c_0_32,hypothesis,
( between(c,e,d)
| between(c,d,e) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
transitivity_for_betweeness ).
cnf(c_0_34,hypothesis,
( outer_pasch(e,c,c,d,d) = c
| between(c,d,e) ),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_35,hypothesis,
~ between(d,e,a),
e_not_between_d_and_a ).
cnf(c_0_36,hypothesis,
( between(X1,e,a)
| ~ between(X1,e,c) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_37,hypothesis,
( outer_pasch(e,c,c,d,d) = c
| outer_pasch(d,c,c,e,e) = c ),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_38,hypothesis,
~ between(d,e,c),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,hypothesis,
( outer_pasch(d,c,c,e,e) = c
| ~ between(c,e,d) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_37]),c_0_20])]),c_0_38]) ).
cnf(c_0_40,negated_conjecture,
~ between(e,d,a),
prove_d_between_e_and_a ).
cnf(c_0_41,hypothesis,
( between(X1,d,a)
| ~ between(X1,d,c) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_42,hypothesis,
outer_pasch(d,c,c,e,e) = c,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_21]) ).
cnf(c_0_43,negated_conjecture,
~ between(e,d,c),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,hypothesis,
~ between(c,d,e),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_42]),c_0_20])]),c_0_43]) ).
cnf(c_0_45,hypothesis,
outer_pasch(e,c,c,d,d) = c,
inference(sr,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_46,hypothesis,
between(c,e,d),
inference(sr,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_47,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_45]),c_0_20]),c_0_46])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO007-1 : TPTP v9.2.1. Bugfixed v2.5.0.
% 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
% 0.14/0.33 % Computer : n028.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 17:36:15 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------