%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO031-3 : 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 : n019.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 04:19:04 PM UTC 2026
% Result : Unsatisfiable 143.90s 100.70s
% Output : CNFRefutation 154.32s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_72)
% Comments :
%------------------------------------------------------------------------------
cnf(r5,axiom,
equidistant(X1,X2,X1,reflection(reflection(X2,X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
cnf(reflection,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax',reflection) ).
cnf(r6,axiom,
X1 = reflection(reflection(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r6) ).
cnf(r2_2,axiom,
equidistant(X1,reflection(X2,X1),X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).
cnf(r2_1,axiom,
between(X1,X2,reflection(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_1) ).
cnf(r4,axiom,
( X2 = X1
| X1 != reflection(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
cnf(r3_1,axiom,
( X2 = reflection(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).
cnf(r3_2,axiom,
X1 = reflection(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_2) ).
cnf(b10,axiom,
( between(X6,inner_pasch(X5,inner_pasch(X1,X6,X4,X5,X3),X1,X2,X3),X3)
| between(X2,inner_pasch(X5,inner_pasch(X1,X6,X4,X5,X3),X1,X2,X3),X5)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3)
| ~ between(X1,X6,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b10) ).
cnf(continuity2,axiom,
( equidistant(X1,X6,X1,continuous(X1,X2,X3,X6,X4,X5))
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',continuity2) ).
cnf(continuity1,axiom,
( between(X3,continuous(X1,X2,X3,X6,X4,X5),X5)
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',continuity1) ).
cnf(euclid3,axiom,
( X1 = X2
| between(euclid1(X1,X4,X2,X5,X3),X3,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',euclid3) ).
cnf(euclid1,axiom,
( X1 = X2
| between(X1,X4,euclid1(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',euclid1) ).
cnf(euclid2,axiom,
( X1 = X2
| between(X1,X5,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',euclid2) ).
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(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(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/sandbox/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(upper_dimension,axiom,
( between(X1,X4,X5)
| between(X4,X5,X1)
| between(X5,X1,X4)
| X2 = X3
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X4,X2,X4,X3)
| ~ equidistant(X5,X2,X5,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',upper_dimension) ).
cnf(e3_2,axiom,
equidistant(X1,extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X3,extension(X4,X3,lower_dimension_point_1,lower_dimension_point_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_2) ).
cnf(d8,axiom,
( equidistant(X1,X5,X3,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
cnf(d5,axiom,
( equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(d10_2,axiom,
( extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4)
| X5 = X6
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
cnf(d11,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X1,X4)
| ~ equidistant(X2,X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11) ).
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(d4_1,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
cnf(d3,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
cnf(d4_2,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
cnf(d2,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
cnf(d4_3,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
cnf(d4_4,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
cnf(d4_5,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
cnf(d9,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(e3_3,axiom,
between(X1,X2,extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_3) ).
cnf(d10_3,axiom,
( extension(X1,X2,X1,X2) = extension(X1,X2,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
cnf(b0,axiom,
( between(X2,X3,X1)
| X1 != extension(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
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(e3_1,axiom,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
cnf(prove_v_to_x_equals_v1_to_x1,negated_conjecture,
~ equidistant(v,x,v1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_to_x_equals_v1_to_x1) ).
cnf(d10_1,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
cnf(e1,axiom,
X1 = extension(X2,X1,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
cnf(d7,axiom,
equidistant(X1,X1,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
cnf(d1,axiom,
equidistant(X1,X2,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(w_to_x_equals_w1_to_x1,hypothesis,
equidistant(w,x,w1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_x_equals_w1_to_x1) ).
cnf(u_to_x_equals_u1_to_x1,hypothesis,
equidistant(u,x,u1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_x_equals_u1_to_x1) ).
cnf(u_to_w_equals_u1_to_w1,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
cnf(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
cnf(b7,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
cnf(b6,axiom,
( between(X1,X3,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
cnf(b9,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
cnf(b8,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
cnf(b5,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
cnf(t6_2,axiom,
( X1 = X2
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_2) ).
cnf(t6_1,axiom,
( X1 = X2
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_1) ).
cnf(b2,axiom,
( X1 = X2
| ~ between(X1,X2,X3)
| ~ between(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
cnf(b3,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
cnf(b1,axiom,
( between(X4,X2,X3)
| ~ between(X1,X2,X3)
| X1 != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
cnf(t1,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension3) ).
cnf(lower_dimension2,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension2) ).
cnf(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension1) ).
cnf(t2,axiom,
between(X1,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
cnf(t3,axiom,
between(X1,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
cnf(v1_between_u1_and_w1,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(e2_2,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
cnf(e2_3,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
cnf(e2_1,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
cnf(i_0_71,axiom,
equidistant(X1,X2,X1,reflection(reflection(X2,X1),X1)),
r5 ).
cnf(i_0_72,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
reflection ).
cnf(i_0_73,axiom,
X1 = reflection(reflection(X1,X2),X2),
r6 ).
cnf(i_0_74,axiom,
equidistant(X1,reflection(X2,X1),X2,X1),
r2_2 ).
cnf(i_0_75,axiom,
between(X1,X2,reflection(X1,X2)),
r2_1 ).
cnf(i_0_76,axiom,
( X2 = X1
| X1 != reflection(X2,X1) ),
r4 ).
cnf(i_0_77,axiom,
( X2 = reflection(X1,X2)
| X1 != X2 ),
r3_1 ).
cnf(i_0_78,axiom,
X1 = reflection(X1,X1),
r3_2 ).
cnf(i_0_79,axiom,
( between(X6,inner_pasch(X5,inner_pasch(X1,X6,X4,X5,X3),X1,X2,X3),X3)
| between(X2,inner_pasch(X5,inner_pasch(X1,X6,X4,X5,X3),X1,X2,X3),X5)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3)
| ~ between(X1,X6,X4) ),
b10,
[final] ).
cnf(i_0_80,axiom,
( equidistant(X1,X6,X1,continuous(X1,X2,X3,X6,X4,X5))
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
continuity2,
[final] ).
cnf(i_0_81,axiom,
( between(X3,continuous(X1,X2,X3,X6,X4,X5),X5)
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
continuity1,
[final] ).
cnf(i_0_82,axiom,
( X1 = X2
| between(euclid1(X1,X4,X2,X5,X3),X3,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid3,
[final] ).
cnf(i_0_83,plain,
equidistant(X1,X2,X1,extension(extension(X2,X1,X2,X1),X1,extension(X2,X1,X2,X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_71,c_0_72]),c_0_72]),
[final] ).
cnf(i_0_84,axiom,
( X1 = X2
| between(X1,X4,euclid1(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid1,
[final] ).
cnf(i_0_85,axiom,
( X1 = X2
| between(X1,X5,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid2,
[final] ).
cnf(i_0_86,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1,
[final] ).
cnf(i_0_87,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2,
[final] ).
cnf(i_0_88,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,
[final] ).
cnf(i_0_89,axiom,
( between(X1,X4,X5)
| between(X4,X5,X1)
| between(X5,X1,X4)
| X2 = X3
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X4,X2,X4,X3)
| ~ equidistant(X5,X2,X5,X3) ),
upper_dimension,
[final] ).
cnf(i_0_90,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_73,c_0_72]),c_0_72]),
[final] ).
cnf(i_0_91,axiom,
equidistant(X1,extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X3,extension(X4,X3,lower_dimension_point_1,lower_dimension_point_2)),
e3_2,
[final] ).
cnf(i_0_92,axiom,
( equidistant(X1,X5,X3,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
d8,
[final] ).
cnf(i_0_93,axiom,
( equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X5,X6) ),
d5,
[final] ).
cnf(i_0_94,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance,
[final] ).
cnf(i_0_95,axiom,
( extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4)
| X5 = X6
| ~ equidistant(X1,X2,X3,X4) ),
d10_2,
[final] ).
cnf(i_0_96,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X1,X4)
| ~ equidistant(X2,X3,X2,X4) ),
d11,
[final] ).
cnf(i_0_97,plain,
equidistant(X1,extension(X2,X1,X2,X1),X2,X1),
inference(rw,[status(thm)],[i_0_74,c_0_72]),
[final] ).
cnf(i_0_98,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2,
[final] ).
cnf(i_0_99,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_1,
[final] ).
cnf(i_0_100,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
d3,
[final] ).
cnf(i_0_101,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_2,
[final] ).
cnf(i_0_102,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d2,
[final] ).
cnf(i_0_103,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_3,
[final] ).
cnf(i_0_104,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d4_4,
[final] ).
cnf(i_0_105,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_5,
[final] ).
cnf(i_0_106,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
d9,
[final] ).
cnf(i_0_107,plain,
between(X1,X2,extension(X1,X2,X1,X2)),
inference(rw,[status(thm)],[i_0_75,c_0_72]),
[final] ).
cnf(i_0_108,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1,
[final] ).
cnf(i_0_109,axiom,
between(X1,X2,extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2)),
e3_3,
[final] ).
cnf(i_0_110,axiom,
( extension(X1,X2,X1,X2) = extension(X1,X2,X2,X1)
| X1 = X2 ),
d10_3,
[final] ).
cnf(i_0_111,axiom,
( between(X2,X3,X1)
| X1 != extension(X2,X3,X4,X5) ),
b0,
[final] ).
cnf(i_0_112,plain,
( X1 = X2
| X1 != extension(X2,X1,X2,X1) ),
inference(rw,[status(thm)],[i_0_76,c_0_72]),
[final] ).
cnf(i_0_113,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance,
[final] ).
cnf(i_0_114,axiom,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
e3_1,
[final] ).
cnf(i_0_115,negated_conjecture,
~ equidistant(v,x,v1,x1),
prove_v_to_x_equals_v1_to_x1,
[final] ).
cnf(i_0_116,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
d10_1,
[final] ).
cnf(i_0_117,plain,
( X2 = extension(X1,X2,X1,X2)
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_77,c_0_72]),
[final] ).
cnf(i_0_118,plain,
X1 = extension(X1,X1,X1,X1),
inference(rw,[status(thm)],[i_0_78,c_0_72]),
[final] ).
cnf(i_0_119,axiom,
X1 = extension(X2,X1,X3,X3),
e1,
[final] ).
cnf(i_0_120,axiom,
equidistant(X1,X1,X2,X2),
d7,
[final] ).
cnf(i_0_121,axiom,
equidistant(X1,X2,X1,X2),
d1,
[final] ).
cnf(i_0_122,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance,
[final] ).
cnf(i_0_123,hypothesis,
equidistant(w,x,w1,x1),
w_to_x_equals_w1_to_x1,
[final] ).
cnf(i_0_124,hypothesis,
equidistant(u,x,u1,x1),
u_to_x_equals_u1_to_x1,
[final] ).
cnf(i_0_125,hypothesis,
equidistant(u,w,u1,w1),
u_to_w_equals_u1_to_w1,
[final] ).
cnf(i_0_126,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1,
[final] ).
cnf(i_0_127,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b7,
[final] ).
cnf(i_0_128,axiom,
( between(X1,X3,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b6,
[final] ).
cnf(i_0_129,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b9,
[final] ).
cnf(i_0_130,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
b8,
[final] ).
cnf(i_0_131,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b5,
[final] ).
cnf(i_0_132,axiom,
( X1 = X2
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
t6_2,
[final] ).
cnf(i_0_133,axiom,
( X1 = X2
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X1,X3) ),
t6_1,
[final] ).
cnf(i_0_134,axiom,
( X1 = X2
| ~ between(X1,X2,X3)
| ~ between(X2,X1,X3) ),
b2,
[final] ).
cnf(i_0_135,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
b3,
[final] ).
cnf(i_0_136,axiom,
( between(X4,X2,X3)
| ~ between(X1,X2,X3)
| X1 != X3 ),
b1,
[final] ).
cnf(i_0_137,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
t1,
[final] ).
cnf(i_0_138,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness,
[final] ).
cnf(i_0_139,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
lower_dimension3,
[final] ).
cnf(i_0_140,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
lower_dimension2,
[final] ).
cnf(i_0_141,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
lower_dimension1,
[final] ).
cnf(i_0_142,axiom,
between(X1,X1,X2),
t2,
[final] ).
cnf(i_0_143,axiom,
between(X1,X2,X2),
t3,
[final] ).
cnf(i_0_144,hypothesis,
between(u1,v1,w1),
v1_between_u1_and_w1,
[final] ).
cnf(i_0_145,hypothesis,
between(u,v,w),
v_between_u_and_w,
[final] ).
cnf(i_0_146,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
e2_2,
[final] ).
cnf(i_0_147,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
e2_3,
[final] ).
cnf(i_0_148,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
e2_1,
[final] ).
cnf(i_0_149,axiom,
X1 = X1 ).
cnf(i_0_150,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_151,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_152,axiom,
( X1 != X2
| extension(X1,X3,X4,X5) = extension(X2,X3,X4,X5) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| extension(X3,X1,X4,X5) = extension(X3,X2,X4,X5) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| extension(X3,X4,X1,X5) = extension(X3,X4,X2,X5) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| extension(X3,X4,X5,X1) = extension(X3,X4,X5,X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| ~ between(X1,X3,X4)
| between(X2,X3,X4) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| ~ between(X3,X1,X4)
| between(X3,X2,X4) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| ~ between(X3,X4,X1)
| between(X3,X4,X2) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| ~ equidistant(X1,X3,X4,X5)
| equidistant(X2,X3,X4,X5) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| ~ equidistant(X3,X1,X4,X5)
| equidistant(X3,X2,X4,X5) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X1,X5)
| equidistant(X3,X4,X2,X5) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X5,X1)
| equidistant(X3,X4,X5,X2) ) ).
cnf(i_0_163,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(equality_inference,[],[111]) ).
cnf(i_0_164,plain,
X1 = extension(X1,X1,X1,X1),
inference(equality_inference,[],[117]) ).
cnf(i_0_166,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(scs_inference,[],[i_0_98,i_0_99]) ).
cnf(i_0_168,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(scs_inference,[],[i_0_98,i_0_99,i_0_100]) ).
cnf(i_0_170,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(scs_inference,[],[i_0_98,i_0_99,i_0_100,i_0_101]) ).
cnf(i_0_172,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(scs_inference,[],[i_0_98,i_0_99,i_0_100,i_0_101,i_0_102]) ).
cnf(i_0_174,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(scs_inference,[],[i_0_98,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103]) ).
cnf(i_0_176,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(scs_inference,[],[i_0_98,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104]) ).
cnf(i_0_178,plain,
equidistant(X1,X2,extension(X3,X4,X2,X1),X4),
inference(scs_inference,[],[i_0_98,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105]) ).
cnf(i_0_180,plain,
between(extension(X1,X2,X1,X2),X2,X1),
inference(scs_inference,[],[i_0_98,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111]) ).
cnf(i_0_182,plain,
extension(X1,X2,X3,X3) = X2,
inference(scs_inference,[],[i_0_98,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113]) ).
cnf(i_0_184,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(scs_inference,[],[i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137]) ).
cnf(i_0_186,plain,
extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2) = X1,
inference(scs_inference,[],[i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150]) ).
cnf(i_0_187,plain,
~ equidistant(v,x,X1,v1),
inference(scs_inference,[],[i_0_115,i_0_122,i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93]) ).
cnf(i_0_188,plain,
equidistant(X1,X2,X2,X1),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_190,plain,
~ equidistant(v1,X1,v,x),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94]) ).
cnf(i_0_191,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_193,plain,
~ equidistant(extension(X1,v,X2,X2),x,v1,X3),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159]) ).
cnf(i_0_194,plain,
~ equidistant(v,extension(extension(x,X1,x,X1),X1,extension(x,X1,x,X1),X1),v1,X2),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160]) ).
cnf(i_0_195,plain,
~ equidistant(v1,X1,extension(X2,v,X3,X3),x),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161]) ).
cnf(i_0_196,plain,
~ equidistant(v1,X1,v,extension(extension(x,X2,x,X2),X2,extension(x,X2,x,X2),X2)),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_98,i_0_108,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161,i_0_162]) ).
cnf(i_0_197,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_3),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_142,i_0_98,i_0_108,i_0_139,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161,i_0_162,i_0_129]) ).
cnf(i_0_198,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_203,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_206,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_209,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_214,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_216,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_218,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_241,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_245,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_248,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_263,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_281,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_285,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_288,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_294,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_321,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_324,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_342,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_359,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_411,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_421,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_426,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_431,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_435,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_474,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_480,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_483,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_503,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_507,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_512,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_513,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_514,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_515,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_517,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_519,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_521,plain,
between(w,v,u),
inference(scs_inference,[],[i_0_145,i_0_137]) ).
cnf(i_0_551,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_557,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_575,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_576,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_618,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_621,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_632,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_634,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_635,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_651,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_653,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_684,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_702,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_725,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_727,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_756,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_798,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_829,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_833,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_865,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_908,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_937,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_997,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_1000,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_1005,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_1069,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1072,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1077,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1080,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1085,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_1154,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1159,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1162,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1165,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1170,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1239,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1244,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1258,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_1310,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_1313,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1316,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1319,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1322,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1325,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1330,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_1387,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1390,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1393,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1405,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_1450,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_1459,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1462,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1465,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1472,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1529,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1532,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1535,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1538,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1543,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1610,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1613,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1616,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1619,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1622,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1625,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1628,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1835,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_1910,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_1992,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1995,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_1998,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2001,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2006,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2012,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_2056,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_2064,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2067,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2070,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2073,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2076,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2079,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_2129,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_2142,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_2369,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_2450,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_2457,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_2523,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_2597,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_2612,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_2742,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_3323,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_3330,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3335,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3338,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3341,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3344,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3347,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3350,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3455,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_3501,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_3531,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3545,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_3675,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_3721,plain,
X1 = extension(extension(X1,X2,X1,X2),X2,extension(X1,X2,X1,X2),X2),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_3798,plain,
equidistant(X1,X2,X1,extension(extension(X2,X1,X2,X1),X1,extension(X2,X1,X2,X1),X1)),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_3807,plain,
equidistant(X1,X2,X2,X1),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_3827,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_3926,plain,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_3930,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_3964,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_3969,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_4044,plain,
equidistant(X1,X2,X1,extension(extension(X2,X1,X2,X1),X1,extension(X2,X1,X2,X1),X1)),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_4086,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_4185,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_4296,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_4299,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_4301,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_4307,plain,
between(X1,X1,X2),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_4318,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_202,plain,
~ between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_1),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_142,i_0_198,i_0_98,i_0_108,i_0_139,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161,i_0_162,i_0_129,i_0_130,i_0_131]) ).
cnf(i_0_205,plain,
~ between(X1,extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X1),
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_142,i_0_198,i_0_143,i_0_98,i_0_108,i_0_114,i_0_139,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161,i_0_162,i_0_129,i_0_130,i_0_131,i_0_134]) ).
cnf(i_0_213,plain,
lower_dimension_point_3 != lower_dimension_point_2,
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_142,i_0_198,i_0_203,i_0_209,i_0_143,i_0_98,i_0_108,i_0_119,i_0_114,i_0_139,i_0_140,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161,i_0_162,i_0_129,i_0_130,i_0_131,i_0_134,i_0_135,i_0_136,i_0_156]) ).
cnf(i_0_215,plain,
lower_dimension_point_3 != lower_dimension_point_1,
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_142,i_0_198,i_0_203,i_0_209,i_0_214,i_0_143,i_0_98,i_0_108,i_0_119,i_0_114,i_0_139,i_0_140,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161,i_0_162,i_0_129,i_0_130,i_0_131,i_0_134,i_0_135,i_0_136,i_0_156,i_0_157]) ).
cnf(i_0_217,plain,
extension(lower_dimension_point_2,lower_dimension_point_1,X1,X2) != lower_dimension_point_2,
inference(scs_inference,[],[i_0_115,i_0_121,i_0_122,i_0_142,i_0_198,i_0_203,i_0_209,i_0_214,i_0_143,i_0_206,i_0_98,i_0_108,i_0_119,i_0_114,i_0_139,i_0_140,i_0_90,i_0_99,i_0_100,i_0_101,i_0_102,i_0_103,i_0_104,i_0_105,i_0_111,i_0_113,i_0_137,i_0_150,i_0_93,i_0_94,i_0_159,i_0_160,i_0_161,i_0_162,i_0_129,i_0_130,i_0_131,i_0_134,i_0_135,i_0_136,i_0_156,i_0_157,i_0_158]) ).
cnf(i_0_219,plain,
between(X1,X2,extension(X3,extension(X1,X2,X4,X5),X6,X6)),
inference(scs_inference,[],[i_0_182,i_0_111]) ).
cnf(i_0_220,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_222,plain,
equidistant(w,x,X1,w1),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_111,i_0_99]) ).
cnf(i_0_224,plain,
equidistant(x,w,w1,X1),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_111,i_0_99,i_0_100]) ).
cnf(i_0_226,plain,
equidistant(x,w,X1,w1),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_111,i_0_99,i_0_100,i_0_101]) ).
cnf(i_0_228,plain,
between(w1,v1,u1),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_144,i_0_111,i_0_99,i_0_100,i_0_101,i_0_137]) ).
cnf(i_0_230,plain,
equidistant(w1,X1,w,x),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_144,i_0_111,i_0_99,i_0_100,i_0_101,i_0_137,i_0_102]) ).
cnf(i_0_232,plain,
equidistant(X1,w1,x,w),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_144,i_0_111,i_0_99,i_0_100,i_0_101,i_0_137,i_0_102,i_0_105]) ).
cnf(i_0_234,plain,
equidistant(w1,X1,x,w),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_144,i_0_111,i_0_99,i_0_100,i_0_101,i_0_137,i_0_102,i_0_105,i_0_103]) ).
cnf(i_0_236,plain,
equidistant(X1,w1,w,x),
inference(scs_inference,[],[i_0_123,i_0_182,i_0_144,i_0_111,i_0_99,i_0_100,i_0_101,i_0_137,i_0_102,i_0_105,i_0_103,i_0_104]) ).
cnf(i_0_239,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_251,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(rename_variables,[],[i_0_184]) ).
cnf(i_0_254,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_257,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_260,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_266,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_268,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_270,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_272,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_274,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_278,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_280,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(rename_variables,[],[i_0_184]) ).
cnf(i_0_282,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_290,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(rename_variables,[],[i_0_184]) ).
cnf(i_0_291,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(rename_variables,[],[i_0_172]) ).
cnf(c_0_237,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
i_0_113 ).
cnf(c_0_238,plain,
equidistant(w,x,X1,w1),
i_0_222 ).
cnf(c_0_239,plain,
equidistant(X1,w1,x,w),
i_0_232 ).
cnf(c_0_240,plain,
w = x,
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_241,plain,
equidistant(X1,w1,x,x),
inference(rw,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_242,axiom,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
i_0_114 ).
cnf(c_0_243,plain,
X1 = w1,
inference(spm,[status(thm)],[c_0_237,c_0_241]) ).
cnf(c_0_244,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_242,c_0_243]),c_0_243]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO031-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 17:37:29 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 143.90/100.70 % Version : CSE_E---1.7
% 143.90/100.70 % Problem : theBenchmark.p
% 143.90/100.70 % SZS status Unsatisfiable for theBenchmark.p
% 143.90/100.70 % SZS output start CNFRefutation
% See solution above
% 154.32/111.14 % Total time : 100.363s
%------------------------------------------------------------------------------