%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO026-2 : TPTP v9.2.1. Released v1.0.0.
% 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 04:19:03 PM UTC 2026
% Result : Unsatisfiable 3.99s 3.18s
% Output : CNFRefutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 17 unt; 5 nHn; 23 RR)
% Number of literals : 64 ( 11 equ; 35 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_equidistance,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(v_to_w_equals_v_to_x,hypothesis,
equidistant(v,w,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v_to_x) ).
cnf(outer_five_segment,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(v_between_u_and_x,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_x) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(u_not_v,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(prove_w_is_x,negated_conjecture,
w != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_is_x) ).
cnf(c_0_9,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_10,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_11,hypothesis,
equidistant(v,w,v,x),
v_to_w_equals_v_to_x ).
cnf(c_0_12,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
( equidistant(X1,X2,v,x)
| ~ equidistant(v,w,X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_14,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
outer_five_segment ).
cnf(c_0_15,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,hypothesis,
equidistant(w,v,v,x),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_17,plain,
( X1 = X2
| equidistant(X3,X4,X5,X4)
| ~ between(X6,X2,X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X2,X3,X2,X5)
| ~ equidistant(X1,X4,X6,X4)
| ~ equidistant(X1,X2,X6,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
equidistant(v,x,v,w),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_19,hypothesis,
( X1 = v
| equidistant(x,X2,w,X2)
| ~ between(X3,v,w)
| ~ between(X1,v,x)
| ~ equidistant(X1,v,X3,v)
| ~ equidistant(X1,X2,X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,hypothesis,
( X1 = v
| equidistant(x,X2,w,X2)
| ~ between(X1,v,w)
| ~ between(X1,v,x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_15])]) ).
cnf(c_0_21,hypothesis,
between(u,v,x),
v_between_u_and_x ).
cnf(c_0_22,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_23,hypothesis,
u != v,
u_not_v ).
cnf(c_0_24,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_25,hypothesis,
equidistant(x,X1,w,X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_26,negated_conjecture,
w != x,
prove_w_is_x ).
cnf(c_0_27,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO026-2 : TPTP v9.2.1. Released v1.0.0.
% 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 17:37:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.99/3.18 % Version : CSE_E---1.7
% 3.99/3.18 % Problem : theBenchmark.p
% 3.99/3.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.99/3.18 % SZS output start CNFRefutation
% See solution above
% 3.99/3.19 % Total time : 2.368s
%------------------------------------------------------------------------------