%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO010-2 : TPTP v9.2.1. Released v1.0.0.
% 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 : n022.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 04:18:58 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 50 ( 13 unt; 6 nHn; 44 RR)
% Number of literals : 115 ( 6 equ; 72 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 86 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_colinear_in_all_orders,negated_conjecture,
( ~ colinear(a,c,b)
| ~ colinear(b,a,c)
| ~ colinear(b,c,a)
| ~ colinear(c,a,b)
| ~ colinear(c,b,a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_colinear_in_all_orders) ).
cnf(colinearity2,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
cnf(colinearity3,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(inner_pasch2,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
cnf(inner_pasch1,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(colinearity4,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
cnf(abc_colinear,hypothesis,
colinear(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abc_colinear) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(colinearity1,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(c_0_12,negated_conjecture,
( ~ colinear(a,c,b)
| ~ colinear(b,a,c)
| ~ colinear(b,c,a)
| ~ colinear(c,a,b)
| ~ colinear(c,b,a) ),
prove_colinear_in_all_orders ).
cnf(c_0_13,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
colinearity2 ).
cnf(c_0_14,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
colinearity3 ).
cnf(c_0_15,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_16,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2 ).
cnf(c_0_17,negated_conjecture,
( ~ colinear(b,a,c)
| ~ colinear(b,c,a)
| ~ colinear(c,a,b)
| ~ between(b,a,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_18,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1 ).
cnf(c_0_19,plain,
( inner_pasch(X1,X2,X3,X1,X4) = X1
| ~ between(X4,X1,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
colinearity4 ).
cnf(c_0_21,hypothesis,
colinear(a,b,c),
abc_colinear ).
cnf(c_0_22,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_23,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_24,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
colinearity1 ).
cnf(c_0_25,negated_conjecture,
( ~ colinear(b,a,c)
| ~ colinear(b,c,a)
| ~ between(b,a,c)
| ~ between(b,c,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( ~ colinear(b,a,c)
| ~ between(b,a,c)
| ~ between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_14]) ).
cnf(c_0_27,plain,
( between(X1,X2,X3)
| ~ between(X3,X2,X4)
| ~ between(X2,X1,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,hypothesis,
( between(a,b,c)
| between(b,c,a)
| between(c,a,b) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_30,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( ~ between(b,a,c)
| ~ between(c,a,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_13]),c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( ~ between(b,a,c)
| ~ between(b,c,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_24]) ).
cnf(c_0_33,negated_conjecture,
( ~ between(b,a,c)
| ~ between(a,b,c) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_34,hypothesis,
( between(b,c,a)
| between(a,b,c)
| between(X1,a,c)
| ~ between(a,X1,b) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
~ between(b,a,c),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_32]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( ~ colinear(a,c,b)
| ~ colinear(b,c,a)
| ~ colinear(c,a,b)
| ~ between(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_14]),c_0_13]) ).
cnf(c_0_38,hypothesis,
( between(a,b,c)
| between(b,c,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( ~ between(a,c,b)
| ~ between(c,a,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_24]),c_0_13]),c_0_24]) ).
cnf(c_0_40,negated_conjecture,
( ~ between(a,c,b)
| ~ between(b,c,a) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_14]),c_0_24]),c_0_24]) ).
cnf(c_0_41,negated_conjecture,
( ~ between(a,c,b)
| ~ between(a,b,c) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_13]),c_0_14]),c_0_24]) ).
cnf(c_0_42,hypothesis,
( between(a,b,c)
| between(X1,c,b)
| ~ between(c,X1,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
~ between(a,c,b),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( ~ colinear(b,c,a)
| ~ colinear(c,a,b)
| ~ between(c,b,a) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_24]),c_0_14]),c_0_13]) ).
cnf(c_0_45,hypothesis,
between(a,b,c),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( ~ between(c,b,a)
| ~ between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_13]),c_0_14]) ).
cnf(c_0_47,hypothesis,
( between(X1,b,a)
| ~ between(b,X1,c) ),
inference(spm,[status(thm)],[c_0_27,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
~ between(c,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_45])]) ).
cnf(c_0_49,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO010-2 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:36:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------