%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO500+1 : TPTP v9.2.1. Released v7.0.0.
% 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 : n020.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 04:21:25 PM UTC 2026
% Result : Theorem 7.28s 5.63s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 161 ( 35 unt; 0 def)
% Number of atoms : 435 ( 125 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 485 ( 211 ~; 243 |; 31 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 407 ( 3 sgn 236 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz7_19,conjecture,
! [X12,X15,X13] :
( s(X12,s(X15,X13)) != s(X15,s(X12,X13))
| X12 = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_19) ).
fof(aSatz7_7,axiom,
! [X12,X13] : s(X12,s(X12,X13)) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_7) ).
fof(aSatz7_9,axiom,
! [X12,X13,X16] :
( s(X12,X13) != s(X12,X16)
| X13 = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_9) ).
fof(aSatz7_10b,axiom,
! [X12,X13] :
( s(X12,X13) = X13
| X13 != X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10b) ).
fof(d_Defn7_1,axiom,
! [X12,X29,X15] :
( ( ~ s_m(X12,X29,X15)
| s_t(X12,X29,X15) )
& ( ~ s_m(X12,X29,X15)
| s_e(X29,X12,X29,X15) )
& ( ~ s_t(X12,X29,X15)
| ~ s_e(X29,X12,X29,X15)
| s_m(X12,X29,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn7_1) ).
fof(aSatz7_18,axiom,
! [X12,X13,X15] :
( s(X12,X13) != s(X15,X13)
| X12 = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_18) ).
fof(aSatz3_4,axiom,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| ~ s_t(X15,X12,X14)
| X12 = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_4) ).
fof(aSatz7_4a,axiom,
! [X13,X12] : s_m(X13,X12,s(X12,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4a) ).
fof(aSatz6_2a,axiom,
! [X12,X13,X15,X14] :
( X12 = X13
| X15 = X13
| X14 = X13
| ~ s_t(X12,X13,X14)
| ~ s_t(X15,X13,X14)
| sameside(X12,X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_2a) ).
fof(aSatz6_3a,axiom,
! [X12,X13,X15] :
( ( ~ sameside(X12,X13,X15)
| X12 != X13 )
& ( ~ sameside(X12,X13,X15)
| X15 != X13 )
& ( ~ sameside(X12,X13,X15)
| c63(X12,X13,X15) != X13 )
& ( ~ sameside(X12,X13,X15)
| s_t(X12,X13,c63(X12,X13,X15)) )
& ( ~ sameside(X12,X13,X15)
| s_t(X15,X13,c63(X12,X13,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_3a) ).
fof(aSatz3_6a,axiom,
! [X12,X15,X14,X17] :
( ~ s_t(X12,X15,X14)
| ~ s_t(X12,X14,X17)
| s_t(X15,X14,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_6a) ).
fof(aSatz6_4b,axiom,
! [X12,X13,X15] :
( sameside(X12,X13,X15)
| ~ s_col(X12,X13,X15)
| s_t(X12,X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4b) ).
fof(d_Defn4_10,axiom,
! [X12,X15,X14] :
( ( ~ s_col(X12,X15,X14)
| s_t(X12,X15,X14)
| s_t(X15,X14,X12)
| s_t(X14,X12,X15) )
& ( s_col(X12,X15,X14)
| ~ s_t(X12,X15,X14) )
& ( s_col(X12,X15,X14)
| ~ s_t(X15,X14,X12) )
& ( s_col(X12,X15,X14)
| ~ s_t(X14,X12,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_10) ).
fof(aSatz7_10a,axiom,
! [X12,X13] :
( s(X12,X13) != X13
| X13 = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10a) ).
fof(aSatz3_2,axiom,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| s_t(X14,X15,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_2) ).
fof(aSatz6_6,axiom,
! [X12,X13,X15] :
( ~ sameside(X12,X13,X15)
| sameside(X15,X13,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_6) ).
fof(aSatz6_5,axiom,
! [X12,X13] :
( X12 = X13
| sameside(X12,X13,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_5) ).
fof(aSatz4_11c,axiom,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X14,X15,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11c) ).
fof(aSatz7_15b,axiom,
! [X13,X16,X27,X12] :
( s_t(X13,X16,X27)
| ~ s_t(s(X12,X13),s(X12,X16),s(X12,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15b) ).
fof(aSatz6_4a,axiom,
! [X12,X13,X15] :
( ( ~ sameside(X12,X13,X15)
| s_col(X12,X13,X15) )
& ( ~ sameside(X12,X13,X15)
| ~ s_t(X12,X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4a) ).
fof(aSatz7_15a,axiom,
! [X13,X16,X27,X12] :
( ~ s_t(X13,X16,X27)
| s_t(s(X12,X13),s(X12,X16),s(X12,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15a) ).
fof(aA2,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ~ s_e(X1,X2,X3,X4)
| ~ s_e(X1,X2,X5,X6)
| s_e(X3,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO011+0.ax',aA2) ).
fof(aSatz7_13,axiom,
! [X13,X16,X12] : s_e(X13,X16,s(X12,X13),s(X12,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_13) ).
fof(aSatz6_16b,axiom,
! [X13,X16,X28,X27] :
( X13 = X16
| X28 = X13
| ~ s_col(X13,X16,X28)
| ~ s_col(X13,X16,X27)
| s_col(X13,X28,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_16b) ).
fof(aSatz4_11a,axiom,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X15,X14,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11a) ).
fof(aSatz4_18,axiom,
! [X12,X15,X14,X22] :
( X12 = X15
| ~ s_col(X12,X15,X14)
| ~ s_e(X12,X14,X12,X22)
| ~ s_e(X15,X14,X15,X22)
| X14 = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_18) ).
fof(aSatz6_7,axiom,
! [X12,X13,X15,X14] :
( ~ sameside(X12,X13,X15)
| ~ sameside(X15,X13,X14)
| sameside(X12,X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_7) ).
fof(c_0_27,negated_conjecture,
~ ! [X12,X15,X13] :
( s(X12,s(X15,X13)) != s(X15,s(X12,X13))
| X12 = X15 ),
inference(assume_negation,[status(cth)],[aSatz7_19]) ).
fof(c_0_28,plain,
! [X873,X874] : s(X873,s(X873,X874)) = X874,
inference(variable_rename,[status(thm)],[aSatz7_7]) ).
fof(c_0_29,negated_conjecture,
( s(esk1_0,s(esk2_0,esk3_0)) = s(esk2_0,s(esk1_0,esk3_0))
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_30,plain,
! [X879,X880,X881] :
( s(X879,X880) != s(X879,X881)
| X880 = X881 ),
inference(variable_rename,[status(thm)],[aSatz7_9]) ).
cnf(c_0_31,plain,
s(X1,s(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
s(esk1_0,s(esk2_0,esk3_0)) = s(esk2_0,s(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_33,plain,
! [X884,X885] :
( s(X884,X885) = X885
| X885 != X884 ),
inference(variable_rename,[status(thm)],[aSatz7_10b]) ).
cnf(c_0_34,plain,
( X2 = X3
| s(X1,X2) != s(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
s(esk1_0,s(esk2_0,s(esk1_0,esk3_0))) = s(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( s(X1,X2) = X2
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( s(esk2_0,s(esk1_0,esk3_0)) = X1
| s(esk1_0,X1) != s(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
s(X1,X1) = X1,
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( s(esk2_0,s(esk1_0,esk3_0)) = esk1_0
| s(esk2_0,esk3_0) != esk1_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_40,plain,
! [X12,X29,X15] :
( ( ~ s_m(X12,X29,X15)
| s_t(X12,X29,X15) )
& ( ~ s_m(X12,X29,X15)
| s_e(X29,X12,X29,X15) )
& ( ~ s_t(X12,X29,X15)
| ~ s_e(X29,X12,X29,X15)
| s_m(X12,X29,X15) ) ),
inference(fof_simplification,[status(thm)],[d_Defn7_1]) ).
cnf(c_0_41,negated_conjecture,
( X1 = s(esk2_0,esk3_0)
| s(esk1_0,X1) != s(esk2_0,s(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_42,negated_conjecture,
( s(esk1_0,esk3_0) = s(esk2_0,esk1_0)
| s(esk2_0,esk3_0) != esk1_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
fof(c_0_43,plain,
! [X911,X912,X913] :
( s(X911,X912) != s(X913,X912)
| X911 = X913 ),
inference(variable_rename,[status(thm)],[aSatz7_18]) ).
fof(c_0_44,plain,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| ~ s_t(X15,X12,X14)
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz3_4]) ).
fof(c_0_45,plain,
! [X962,X963,X964] :
( ( ~ s_m(X962,X963,X964)
| s_t(X962,X963,X964) )
& ( ~ s_m(X962,X963,X964)
| s_e(X963,X962,X963,X964) )
& ( ~ s_t(X962,X963,X964)
| ~ s_e(X963,X962,X963,X964)
| s_m(X962,X963,X964) ) ),
inference(variable_rename,[status(thm)],[c_0_40]) ).
fof(c_0_46,plain,
! [X864,X865] : s_m(X864,X865,s(X865,X864)),
inference(variable_rename,[status(thm)],[aSatz7_4a]) ).
cnf(c_0_47,negated_conjecture,
( X1 = s(esk2_0,esk3_0)
| s(esk2_0,esk3_0) != esk1_0
| s(esk1_0,X1) != esk1_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_31]) ).
cnf(c_0_48,plain,
( X1 = X3
| s(X1,X2) != s(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_49,plain,
! [X12,X13,X15,X14] :
( X12 = X13
| X15 = X13
| X14 = X13
| ~ s_t(X12,X13,X14)
| ~ s_t(X15,X13,X14)
| sameside(X12,X13,X15) ),
inference(fof_simplification,[status(thm)],[aSatz6_2a]) ).
fof(c_0_50,plain,
! [X12,X13,X15] :
( ( ~ sameside(X12,X13,X15)
| X12 != X13 )
& ( ~ sameside(X12,X13,X15)
| X15 != X13 )
& ( ~ sameside(X12,X13,X15)
| c63(X12,X13,X15) != X13 )
& ( ~ sameside(X12,X13,X15)
| s_t(X12,X13,c63(X12,X13,X15)) )
& ( ~ sameside(X12,X13,X15)
| s_t(X15,X13,c63(X12,X13,X15)) ) ),
inference(fof_simplification,[status(thm)],[aSatz6_3a]) ).
fof(c_0_51,plain,
! [X12,X15,X14,X17] :
( ~ s_t(X12,X15,X14)
| ~ s_t(X12,X14,X17)
| s_t(X15,X14,X17) ),
inference(fof_simplification,[status(thm)],[aSatz3_6a]) ).
fof(c_0_52,plain,
! [X12,X13,X15] :
( sameside(X12,X13,X15)
| ~ s_col(X12,X13,X15)
| s_t(X12,X13,X15) ),
inference(fof_simplification,[status(thm)],[aSatz6_4b]) ).
fof(c_0_53,plain,
! [X12,X15,X14] :
( ( ~ s_col(X12,X15,X14)
| s_t(X12,X15,X14)
| s_t(X15,X14,X12)
| s_t(X14,X12,X15) )
& ( s_col(X12,X15,X14)
| ~ s_t(X12,X15,X14) )
& ( s_col(X12,X15,X14)
| ~ s_t(X15,X14,X12) )
& ( s_col(X12,X15,X14)
| ~ s_t(X14,X12,X15) ) ),
inference(fof_simplification,[status(thm)],[d_Defn4_10]) ).
fof(c_0_54,plain,
! [X589,X590,X591] :
( ~ s_t(X589,X590,X591)
| ~ s_t(X590,X589,X591)
| X589 = X590 ),
inference(variable_rename,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
( s_t(X1,X2,X3)
| ~ s_m(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
s_m(X1,X2,s(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_57,plain,
! [X882,X883] :
( s(X882,X883) != X883
| X883 = X882 ),
inference(variable_rename,[status(thm)],[aSatz7_10a]) ).
cnf(c_0_58,negated_conjecture,
( s(esk2_0,s(esk1_0,esk3_0)) = s(esk2_0,esk3_0)
| s(esk2_0,esk3_0) != esk1_0 ),
inference(spm,[status(thm)],[c_0_47,c_0_35]) ).
cnf(c_0_59,plain,
( X1 = X2
| s(X1,s(X2,X3)) != X3 ),
inference(spm,[status(thm)],[c_0_48,c_0_31]) ).
cnf(c_0_60,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_61,plain,
! [X762,X763,X764,X765] :
( X762 = X763
| X764 = X763
| X765 = X763
| ~ s_t(X762,X763,X765)
| ~ s_t(X764,X763,X765)
| sameside(X762,X763,X764) ),
inference(variable_rename,[status(thm)],[c_0_49]) ).
fof(c_0_62,plain,
! [X770,X771,X772] :
( ( ~ sameside(X770,X771,X772)
| X770 != X771 )
& ( ~ sameside(X770,X771,X772)
| X772 != X771 )
& ( ~ sameside(X770,X771,X772)
| c63(X770,X771,X772) != X771 )
& ( ~ sameside(X770,X771,X772)
| s_t(X770,X771,c63(X770,X771,X772)) )
& ( ~ sameside(X770,X771,X772)
| s_t(X772,X771,c63(X770,X771,X772)) ) ),
inference(variable_rename,[status(thm)],[c_0_50]) ).
fof(c_0_63,plain,
! [X596,X597,X598,X599] :
( ~ s_t(X596,X597,X598)
| ~ s_t(X596,X598,X599)
| s_t(X597,X598,X599) ),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_64,plain,
! [X780,X781,X782] :
( sameside(X780,X781,X782)
| ~ s_col(X780,X781,X782)
| s_t(X780,X781,X782) ),
inference(variable_rename,[status(thm)],[c_0_52]) ).
fof(c_0_65,plain,
! [X943,X944,X945] :
( ( ~ s_col(X943,X944,X945)
| s_t(X943,X944,X945)
| s_t(X944,X945,X943)
| s_t(X945,X943,X944) )
& ( s_col(X943,X944,X945)
| ~ s_t(X943,X944,X945) )
& ( s_col(X943,X944,X945)
| ~ s_t(X944,X945,X943) )
& ( s_col(X943,X944,X945)
| ~ s_t(X945,X943,X944) ) ),
inference(variable_rename,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
( X1 = X2
| ~ s_t(X1,X2,X3)
| ~ s_t(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
s_t(X1,X2,s(X2,X1)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,plain,
( X2 = X1
| s(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,negated_conjecture,
( s(esk1_0,esk3_0) = esk3_0
| s(esk2_0,esk3_0) != esk1_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_58]),c_0_31]) ).
cnf(c_0_70,negated_conjecture,
( s(esk2_0,esk3_0) != esk1_0
| esk3_0 != esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_39]),c_0_60]) ).
cnf(c_0_71,plain,
( X1 = X2
| X3 = X2
| X4 = X2
| sameside(X1,X2,X3)
| ~ s_t(X1,X2,X4)
| ~ s_t(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,plain,
( s_t(X1,X2,c63(X1,X2,X3))
| ~ sameside(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( ~ sameside(X1,X2,X3)
| c63(X1,X2,X3) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_74,plain,
( s_t(X2,X3,X4)
| ~ s_t(X1,X2,X3)
| ~ s_t(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_75,plain,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| s_t(X14,X15,X12) ),
inference(fof_simplification,[status(thm)],[aSatz3_2]) ).
fof(c_0_76,plain,
! [X12,X13,X15] :
( ~ sameside(X12,X13,X15)
| sameside(X15,X13,X12) ),
inference(fof_simplification,[status(thm)],[aSatz6_6]) ).
cnf(c_0_77,plain,
( sameside(X1,X2,X3)
| s_t(X1,X2,X3)
| ~ s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_78,plain,
( s_col(X1,X2,X3)
| ~ s_t(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_79,plain,
( X1 = X2
| ~ s_t(X1,X2,s(X1,X2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_80,negated_conjecture,
s(esk2_0,esk3_0) != esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_81,plain,
( X1 = X2
| X2 = X3
| sameside(X1,X2,X3)
| ~ sameside(X3,X2,X4)
| ~ s_t(X1,X2,c63(X3,X2,X4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_82,plain,
( s_t(X1,X2,c63(X3,X2,X4))
| ~ sameside(X3,X2,X4)
| ~ s_t(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_72]) ).
fof(c_0_83,plain,
! [X783,X784] :
( X783 = X784
| sameside(X783,X784,X783) ),
inference(variable_rename,[status(thm)],[aSatz6_5]) ).
fof(c_0_84,plain,
! [X584,X585,X586] :
( ~ s_t(X584,X585,X586)
| s_t(X586,X585,X584) ),
inference(variable_rename,[status(thm)],[c_0_75]) ).
fof(c_0_85,plain,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X14,X15,X12) ),
inference(fof_simplification,[status(thm)],[aSatz4_11c]) ).
fof(c_0_86,plain,
! [X13,X16,X27,X12] :
( s_t(X13,X16,X27)
| ~ s_t(s(X12,X13),s(X12,X16),s(X12,X27)) ),
inference(fof_simplification,[status(thm)],[aSatz7_15b]) ).
fof(c_0_87,plain,
! [X12,X13,X15] :
( ( ~ sameside(X12,X13,X15)
| s_col(X12,X13,X15) )
& ( ~ sameside(X12,X13,X15)
| ~ s_t(X12,X13,X15) ) ),
inference(fof_simplification,[status(thm)],[aSatz6_4a]) ).
fof(c_0_88,plain,
! [X785,X786,X787] :
( ~ sameside(X785,X786,X787)
| sameside(X787,X786,X785) ),
inference(variable_rename,[status(thm)],[c_0_76]) ).
cnf(c_0_89,plain,
( sameside(X1,X2,X3)
| s_t(X1,X2,X3)
| ~ s_t(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_90,negated_conjecture,
s_t(s(esk2_0,s(esk1_0,esk3_0)),esk1_0,s(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_67,c_0_35]) ).
cnf(c_0_91,negated_conjecture,
~ s_t(esk1_0,s(esk2_0,esk3_0),s(esk2_0,s(esk1_0,esk3_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_32]),c_0_80]) ).
fof(c_0_92,plain,
! [X13,X16,X27,X12] :
( ~ s_t(X13,X16,X27)
| s_t(s(X12,X13),s(X12,X16),s(X12,X27)) ),
inference(fof_simplification,[status(thm)],[aSatz7_15a]) ).
cnf(c_0_93,plain,
( X1 = X2
| X3 = X1
| sameside(X3,X1,X2)
| ~ sameside(X2,X1,X4)
| ~ s_t(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_94,plain,
( X1 = X2
| sameside(X1,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_95,plain,
( s_t(X3,X2,X1)
| ~ s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_96,plain,
! [X657,X658,X659] :
( ~ s_col(X657,X658,X659)
| s_col(X659,X658,X657) ),
inference(variable_rename,[status(thm)],[c_0_85]) ).
fof(c_0_97,plain,
! [X893,X894,X895,X896] :
( s_t(X893,X894,X895)
| ~ s_t(s(X896,X893),s(X896,X894),s(X896,X895)) ),
inference(variable_rename,[status(thm)],[c_0_86]) ).
fof(c_0_98,plain,
! [X777,X778,X779] :
( ( ~ sameside(X777,X778,X779)
| s_col(X777,X778,X779) )
& ( ~ sameside(X777,X778,X779)
| ~ s_t(X777,X778,X779) ) ),
inference(variable_rename,[status(thm)],[c_0_87]) ).
cnf(c_0_99,plain,
( sameside(X3,X2,X1)
| ~ sameside(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_100,negated_conjecture,
sameside(esk1_0,s(esk2_0,esk3_0),s(esk2_0,s(esk1_0,esk3_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
fof(c_0_101,plain,
! [X889,X890,X891,X892] :
( ~ s_t(X889,X890,X891)
| s_t(s(X892,X889),s(X892,X890),s(X892,X891)) ),
inference(variable_rename,[status(thm)],[c_0_92]) ).
fof(c_0_102,plain,
! [X1,X2,X3,X4,X5,X6] :
( ~ s_e(X1,X2,X3,X4)
| ~ s_e(X1,X2,X5,X6)
| s_e(X3,X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[aA2]) ).
fof(c_0_103,plain,
! [X886,X887,X888] : s_e(X886,X887,s(X888,X886),s(X888,X887)),
inference(variable_rename,[status(thm)],[aSatz7_13]) ).
fof(c_0_104,plain,
! [X13,X16,X28,X27] :
( X13 = X16
| X28 = X13
| ~ s_col(X13,X16,X28)
| ~ s_col(X13,X16,X27)
| s_col(X13,X28,X27) ),
inference(fof_simplification,[status(thm)],[aSatz6_16b]) ).
fof(c_0_105,plain,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X15,X14,X12) ),
inference(fof_simplification,[status(thm)],[aSatz4_11a]) ).
cnf(c_0_106,plain,
( X1 = X2
| X2 = X3
| sameside(X1,X2,X3)
| ~ s_t(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_107,plain,
s_t(s(X1,X2),X1,X2),
inference(spm,[status(thm)],[c_0_95,c_0_67]) ).
cnf(c_0_108,plain,
( s_col(X3,X2,X1)
| ~ s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_109,plain,
( s_t(X1,X2,X3)
| ~ s_t(s(X4,X1),s(X4,X2),s(X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_110,plain,
( ~ sameside(X1,X2,X3)
| ~ s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_111,negated_conjecture,
sameside(s(esk2_0,s(esk1_0,esk3_0)),s(esk2_0,esk3_0),esk1_0),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_112,plain,
( s_t(s(X4,X1),s(X4,X2),s(X4,X3))
| ~ s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
fof(c_0_113,plain,
! [X508,X509,X510,X511,X512,X513] :
( ~ s_e(X508,X509,X510,X511)
| ~ s_e(X508,X509,X512,X513)
| s_e(X510,X511,X512,X513) ),
inference(variable_rename,[status(thm)],[c_0_102]) ).
cnf(c_0_114,plain,
s_e(X1,X2,s(X3,X1),s(X3,X2)),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
fof(c_0_115,plain,
! [X828,X829,X830,X831] :
( X828 = X829
| X830 = X828
| ~ s_col(X828,X829,X830)
| ~ s_col(X828,X829,X831)
| s_col(X828,X830,X831) ),
inference(variable_rename,[status(thm)],[c_0_104]) ).
fof(c_0_116,plain,
! [X651,X652,X653] :
( ~ s_col(X651,X652,X653)
| s_col(X652,X653,X651) ),
inference(variable_rename,[status(thm)],[c_0_105]) ).
cnf(c_0_117,plain,
( s_col(X1,X2,X3)
| ~ sameside(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_118,plain,
( X1 = X2
| sameside(X1,X2,s(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_68]) ).
cnf(c_0_119,plain,
( s_col(X1,X2,X3)
| ~ s_t(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_108,c_0_78]) ).
cnf(c_0_120,plain,
( s_t(X1,s(X2,X3),X4)
| ~ s_t(s(X2,X1),X3,s(X2,X4)) ),
inference(spm,[status(thm)],[c_0_109,c_0_31]) ).
cnf(c_0_121,negated_conjecture,
~ s_t(s(esk2_0,s(esk1_0,esk3_0)),s(esk2_0,esk3_0),esk1_0),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_122,plain,
( s_t(s(X1,X2),s(X1,X3),X4)
| ~ s_t(X2,X3,s(X1,X4)) ),
inference(spm,[status(thm)],[c_0_112,c_0_31]) ).
fof(c_0_123,plain,
! [X12,X15,X14,X22] :
( X12 = X15
| ~ s_col(X12,X15,X14)
| ~ s_e(X12,X14,X12,X22)
| ~ s_e(X15,X14,X15,X22)
| X14 = X22 ),
inference(fof_simplification,[status(thm)],[aSatz4_18]) ).
cnf(c_0_124,plain,
( s_e(X3,X4,X5,X6)
| ~ s_e(X1,X2,X3,X4)
| ~ s_e(X1,X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_125,plain,
s_e(X1,s(X2,X3),s(X2,X1),X3),
inference(spm,[status(thm)],[c_0_114,c_0_31]) ).
cnf(c_0_126,negated_conjecture,
s_e(X1,s(esk2_0,esk3_0),s(esk1_0,X1),s(esk2_0,s(esk1_0,esk3_0))),
inference(spm,[status(thm)],[c_0_114,c_0_32]) ).
cnf(c_0_127,plain,
( X1 = X2
| X3 = X1
| s_col(X1,X3,X4)
| ~ s_col(X1,X2,X3)
| ~ s_col(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_128,plain,
( s_col(X1,X2,X3)
| ~ s_t(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_129,plain,
( s_col(X2,X3,X1)
| ~ s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_130,plain,
( X1 = X2
| s_col(X1,X2,s(X1,X2)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
fof(c_0_131,plain,
! [X12,X13,X15,X14] :
( ~ sameside(X12,X13,X15)
| ~ sameside(X15,X13,X14)
| sameside(X12,X13,X14) ),
inference(fof_simplification,[status(thm)],[aSatz6_7]) ).
cnf(c_0_132,plain,
( sameside(X1,X2,X3)
| s_t(X1,X2,X3)
| ~ s_t(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_119]) ).
cnf(c_0_133,negated_conjecture,
s_t(s(esk1_0,esk3_0),s(esk2_0,esk1_0),esk3_0),
inference(spm,[status(thm)],[c_0_120,c_0_90]) ).
cnf(c_0_134,negated_conjecture,
~ s_t(s(esk1_0,esk3_0),esk3_0,s(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
fof(c_0_135,plain,
! [X694,X695,X696,X697] :
( X694 = X695
| ~ s_col(X694,X695,X696)
| ~ s_e(X694,X696,X694,X697)
| ~ s_e(X695,X696,X695,X697)
| X696 = X697 ),
inference(variable_rename,[status(thm)],[c_0_123]) ).
cnf(c_0_136,plain,
( s_e(X1,X2,s(X3,X4),X5)
| ~ s_e(X4,s(X3,X5),X1,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_137,negated_conjecture,
s_e(esk1_0,s(esk2_0,esk3_0),esk1_0,s(esk2_0,s(esk1_0,esk3_0))),
inference(spm,[status(thm)],[c_0_126,c_0_38]) ).
cnf(c_0_138,plain,
( X1 = X2
| X1 = X3
| s_col(X1,X3,X4)
| ~ s_col(X1,X2,X3)
| ~ s_t(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_139,plain,
( X1 = X2
| s_col(X2,s(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
fof(c_0_140,plain,
! [X788,X789,X790,X791] :
( ~ sameside(X788,X789,X790)
| ~ sameside(X790,X789,X791)
| sameside(X788,X789,X791) ),
inference(variable_rename,[status(thm)],[c_0_131]) ).
cnf(c_0_141,negated_conjecture,
sameside(s(esk1_0,esk3_0),esk3_0,s(esk2_0,esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]) ).
cnf(c_0_142,plain,
( X1 = X2
| X3 = X4
| ~ s_col(X1,X2,X3)
| ~ s_e(X1,X3,X1,X4)
| ~ s_e(X2,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_143,plain,
s_e(X1,X2,X1,s(X1,X2)),
inference(spm,[status(thm)],[c_0_114,c_0_38]) ).
cnf(c_0_144,negated_conjecture,
s_e(esk1_0,s(esk2_0,s(esk1_0,esk3_0)),s(esk2_0,esk1_0),esk3_0),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_145,plain,
( X1 = X2
| s_col(X1,X2,X3)
| ~ s_t(s(X2,X1),X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_68]) ).
cnf(c_0_146,plain,
( sameside(X1,X2,X4)
| ~ sameside(X1,X2,X3)
| ~ sameside(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_147,negated_conjecture,
sameside(s(esk2_0,esk1_0),esk3_0,s(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_99,c_0_141]) ).
cnf(c_0_148,plain,
( s(X1,X2) = X2
| X3 = X1
| ~ s_col(X3,X1,X2)
| ~ s_e(X3,X2,X3,s(X1,X2)) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_149,negated_conjecture,
s_e(s(esk2_0,esk1_0),esk3_0,s(esk2_0,esk1_0),s(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_136,c_0_144]) ).
cnf(c_0_150,negated_conjecture,
( esk3_0 = esk1_0
| s_col(esk3_0,esk1_0,s(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_145,c_0_133]) ).
cnf(c_0_151,negated_conjecture,
( sameside(X1,esk3_0,s(esk1_0,esk3_0))
| ~ sameside(X1,esk3_0,s(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,negated_conjecture,
( s(esk2_0,esk1_0) = esk1_0
| s(esk1_0,esk3_0) = esk3_0
| ~ s_col(s(esk2_0,esk1_0),esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_153,negated_conjecture,
( esk3_0 = esk1_0
| s_col(s(esk2_0,esk1_0),esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_108,c_0_150]) ).
cnf(c_0_154,negated_conjecture,
( sameside(s(esk1_0,esk3_0),esk3_0,X1)
| ~ sameside(X1,esk3_0,s(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_99,c_0_151]) ).
cnf(c_0_155,negated_conjecture,
( s(esk2_0,esk1_0) = esk1_0
| esk3_0 = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_68]) ).
cnf(c_0_156,plain,
( ~ sameside(X1,X2,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_157,negated_conjecture,
sameside(s(esk1_0,esk3_0),esk3_0,s(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_154,c_0_141]) ).
cnf(c_0_158,negated_conjecture,
esk3_0 = esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_155]),c_0_60]) ).
cnf(c_0_159,plain,
~ sameside(X1,X1,X2),
inference(er,[status(thm)],[c_0_156]) ).
cnf(c_0_160,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_158]),c_0_38]),c_0_158]),c_0_158]),c_0_38]),c_0_159]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO500+1 : TPTP v9.2.1. Released v7.0.0.
% 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
% 0.16/0.32 % Computer : n020.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 18:00:05 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 7.28/5.63 % Version : CSE_E---1.7
% 7.28/5.63 % Problem : theBenchmark.p
% 7.28/5.63 % SZS status Theorem for theBenchmark.p
% 7.28/5.63 % SZS output start CNFRefutation
% See solution above
% 7.28/5.66 % Total time : 4.377s
%------------------------------------------------------------------------------