%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO497+1 : TPTP v9.2.1. Released v7.0.0.
% 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 : 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 04:21:25 PM UTC 2026
% Result : Theorem 147.78s 107.13s
% Output : CNFRefutation 148.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 114 ( 33 unt; 0 def)
% Number of atoms : 348 ( 111 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 406 ( 172 ~; 195 |; 39 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 386 ( 14 sgn 206 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz2_2,axiom,
! [X12,X15,X14,X17] :
( ~ s_e(X12,X15,X14,X17)
| s_e(X14,X17,X12,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_2) ).
fof(d_Defn6_1,axiom,
! [X12,X13,X15] :
( ( ~ sameside(X12,X13,X15)
| X12 != X13 )
& ( ~ sameside(X12,X13,X15)
| X15 != X13 )
& ( ~ sameside(X12,X13,X15)
| s_t(X13,X12,X15)
| s_t(X13,X15,X12) )
& ( ~ s_t(X13,X12,X15)
| X12 = X13
| xb = X13
| sameside(X12,X13,X15) )
& ( ~ s_t(X13,X15,X12)
| X12 = X13
| X15 = X13
| sameside(X12,X13,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn6_1) ).
fof(aSatz2_12,axiom,
! [X16,X12,X17,X15,X14] :
( X16 = X12
| ~ s_t(X16,X12,X17)
| ~ s_e(X12,X17,X15,X14)
| X17 = ext(X16,X12,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_12) ).
fof(aNarbouxLemma1,axiom,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| ~ s_e(X12,X14,X12,X15)
| X14 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNarbouxLemma1) ).
fof(aA4,axiom,
! [X1,X2,X7,X4] :
( s_t(X1,X2,ext(X1,X2,X7,X4))
& s_e(X2,ext(X1,X2,X7,X4),X7,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax',aA4) ).
fof(d_Defn5_4,axiom,
! [X12,X15,X14,X17,X2] :
( ( ~ le(X12,X15,X14,X17)
| s_t(X14,insert(X12,X15,X14,X17),X17) )
& ( ~ le(X12,X15,X14,X17)
| s_e(X12,X15,X14,insert(X12,X15,X14,X17)) )
& ( ~ s_t(X14,X2,X17)
| ~ s_e(X12,X15,X14,X2)
| le(X12,X15,X14,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn5_4) ).
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/sandbox2/benchmark/theBenchmark.p',aSatz6_4a) ).
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/sandbox2/benchmark/theBenchmark.p',aSatz3_6a) ).
fof(aSatz5_5b,axiom,
! [X12,X15,X14,X17,X18] :
( le(X12,X15,X14,X17)
| ~ s_t(X12,X15,X18)
| ~ s_e(X12,X18,X14,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5b) ).
fof(aA1,axiom,
! [X1,X2] : s_e(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax',aA1) ).
fof(d_insert,axiom,
! [X12,X15,X20,X22] : insert(X12,X15,X20,X22) = ext(ext(X22,X20,alpha,gamma),X20,X12,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_insert) ).
fof(aA3,axiom,
! [X1,X2,X3] :
( ~ s_e(X1,X2,X3,X3)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax',aA3) ).
fof(aSatz5_7,axiom,
! [X12,X15] : le(X12,X15,X12,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_7) ).
fof(aSatz5_5a,axiom,
! [X12,X15,X14,X17] :
( ( ~ le(X12,X15,X14,X17)
| s_t(X12,X15,ins(X14,X17,X12,X15)) )
& ( ~ le(X12,X15,X14,X17)
| s_e(X12,ins(X14,X17,X12,X15),X14,X17) )
& ( ~ le(X12,X15,X14,X17)
| ins(X14,X17,X12,X15) = ext(X12,X15,insert(X12,X15,X14,X17),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5a) ).
fof(aSatz3_1,axiom,
! [X12,X15] : s_t(X12,X15,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_1) ).
fof(aSatz3_14b,axiom,
! [X15,X12] : X15 != ext(X12,X15,alpha,gamma),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_14b) ).
fof(aSatz6_11a,conjecture,
! [X27,X12,X15,X14] :
( ( X27 = X12
| X15 = X14
| sameside(insert(X15,X14,X12,X27),X12,X27) )
& ( X27 = X12
| X15 = X14
| s_e(X12,insert(X15,X14,X12,X27),X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_11a) ).
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/sandbox2/benchmark/theBenchmark.p',aSatz6_2a) ).
fof(aSatz3_2,axiom,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| s_t(X14,X15,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_2) ).
fof(aSatz5_6,axiom,
! [X12,X15,X14,X17,X20,X21,X22,X26] :
( ~ le(X12,X15,X14,X17)
| ~ s_e(X12,X15,X20,X21)
| ~ s_e(X14,X17,X22,X26)
| le(X20,X21,X22,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_6) ).
fof(aSatz3_3,axiom,
! [X20,X21] : s_t(X20,X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_3) ).
fof(c_0_21,plain,
! [X12,X15,X14,X17] :
( ~ s_e(X12,X15,X14,X17)
| s_e(X14,X17,X12,X15) ),
inference(fof_simplification,[status(thm)],[aSatz2_2]) ).
fof(c_0_22,plain,
! [X12,X13,X15] :
( ( ~ sameside(X12,X13,X15)
| X12 != X13 )
& ( ~ sameside(X12,X13,X15)
| X15 != X13 )
& ( ~ sameside(X12,X13,X15)
| s_t(X13,X12,X15)
| s_t(X13,X15,X12) )
& ( ~ s_t(X13,X12,X15)
| X12 = X13
| xb = X13
| sameside(X12,X13,X15) )
& ( ~ s_t(X13,X15,X12)
| X12 = X13
| X15 = X13
| sameside(X12,X13,X15) ) ),
inference(fof_simplification,[status(thm)],[d_Defn6_1]) ).
fof(c_0_23,plain,
! [X16,X12,X17,X15,X14] :
( X16 = X12
| ~ s_t(X16,X12,X17)
| ~ s_e(X12,X17,X15,X14)
| X17 = ext(X16,X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz2_12]) ).
fof(c_0_24,plain,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| ~ s_e(X12,X14,X12,X15)
| X14 = X15 ),
inference(fof_simplification,[status(thm)],[aNarbouxLemma1]) ).
fof(c_0_25,plain,
! [X403,X404,X405,X406] :
( ~ s_e(X403,X404,X405,X406)
| s_e(X405,X406,X403,X404) ),
inference(variable_rename,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X382,X383,X384,X385] :
( s_t(X382,X383,ext(X382,X383,X384,X385))
& s_e(X383,ext(X382,X383,X384,X385),X384,X385) ),
inference(variable_rename,[status(thm)],[aA4]) ).
fof(c_0_27,plain,
! [X12,X15,X14,X17,X2] :
( ( ~ le(X12,X15,X14,X17)
| s_t(X14,insert(X12,X15,X14,X17),X17) )
& ( ~ le(X12,X15,X14,X17)
| s_e(X12,X15,X14,insert(X12,X15,X14,X17)) )
& ( ~ s_t(X14,X2,X17)
| ~ s_e(X12,X15,X14,X2)
| le(X12,X15,X14,X17) ) ),
inference(fof_simplification,[status(thm)],[d_Defn5_4]) ).
fof(c_0_28,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_29,plain,
! [X703,X704,X705] :
( ( ~ sameside(X703,X704,X705)
| X703 != X704 )
& ( ~ sameside(X703,X704,X705)
| X705 != X704 )
& ( ~ sameside(X703,X704,X705)
| s_t(X704,X703,X705)
| s_t(X704,X705,X703) )
& ( ~ s_t(X704,X703,X705)
| X703 = X704
| xb = X704
| sameside(X703,X704,X705) )
& ( ~ s_t(X704,X705,X703)
| X703 = X704
| X705 = X704
| sameside(X703,X704,X705) ) ),
inference(variable_rename,[status(thm)],[c_0_22]) ).
fof(c_0_30,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_31,plain,
! [X12,X15,X14,X17,X18] :
( le(X12,X15,X14,X17)
| ~ s_t(X12,X15,X18)
| ~ s_e(X12,X18,X14,X17) ),
inference(fof_simplification,[status(thm)],[aSatz5_5b]) ).
fof(c_0_32,plain,
! [X429,X430,X431,X432,X433] :
( X429 = X430
| ~ s_t(X429,X430,X431)
| ~ s_e(X430,X431,X432,X433)
| X431 = ext(X429,X430,X432,X433) ),
inference(variable_rename,[status(thm)],[c_0_23]) ).
fof(c_0_33,plain,
! [X371,X372] : s_e(X371,X372,X372,X371),
inference(variable_rename,[status(thm)],[aA1]) ).
fof(c_0_34,plain,
! [X621,X622,X623] :
( ~ s_t(X621,X622,X623)
| ~ s_e(X621,X623,X621,X622)
| X623 = X622 ),
inference(variable_rename,[status(thm)],[c_0_24]) ).
cnf(c_0_35,plain,
( s_e(X3,X4,X1,X2)
| ~ s_e(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
s_e(X1,ext(X2,X1,X3,X4),X3,X4),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_37,plain,
! [X698,X699,X700,X701,X702] :
( ( ~ le(X698,X699,X700,X701)
| s_t(X700,insert(X698,X699,X700,X701),X701) )
& ( ~ le(X698,X699,X700,X701)
| s_e(X698,X699,X700,insert(X698,X699,X700,X701)) )
& ( ~ s_t(X700,X702,X701)
| ~ s_e(X698,X699,X700,X702)
| le(X698,X699,X700,X701) ) ),
inference(variable_rename,[status(thm)],[c_0_27]) ).
fof(c_0_38,plain,
! [X661,X662,X663,X664] : insert(X661,X662,X663,X664) = ext(ext(X664,X663,alpha,gamma),X663,X661,X662),
inference(variable_rename,[status(thm)],[d_insert]) ).
fof(c_0_39,plain,
! [X642,X643,X644] :
( ( ~ sameside(X642,X643,X644)
| s_col(X642,X643,X644) )
& ( ~ sameside(X642,X643,X644)
| ~ s_t(X642,X643,X644) ) ),
inference(variable_rename,[status(thm)],[c_0_28]) ).
cnf(c_0_40,plain,
( X3 = X1
| X2 = X1
| sameside(X3,X1,X2)
| ~ s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,plain,
s_t(X1,X2,ext(X1,X2,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_42,plain,
! [X461,X462,X463,X464] :
( ~ s_t(X461,X462,X463)
| ~ s_t(X461,X463,X464)
| s_t(X462,X463,X464) ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
fof(c_0_43,plain,
! [X1,X2,X3] :
( ~ s_e(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[aA3]) ).
fof(c_0_44,plain,
! [X583,X584,X585,X586,X587] :
( le(X583,X584,X585,X586)
| ~ s_t(X583,X584,X587)
| ~ s_e(X583,X587,X585,X586) ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
cnf(c_0_45,plain,
( X1 = X2
| X3 = ext(X1,X2,X4,X5)
| ~ s_t(X1,X2,X3)
| ~ s_e(X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_46,plain,
s_e(X1,X2,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_47,plain,
( X3 = X2
| ~ s_t(X1,X2,X3)
| ~ s_e(X1,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,plain,
s_e(X1,X2,X3,ext(X4,X3,X1,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_49,plain,
( s_t(X3,insert(X1,X2,X3,X4),X4)
| ~ le(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
insert(X1,X2,X3,X4) = ext(ext(X4,X3,alpha,gamma),X3,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_51,plain,
! [X596,X597] : le(X596,X597,X596,X597),
inference(variable_rename,[status(thm)],[aSatz5_7]) ).
cnf(c_0_52,plain,
( ~ sameside(X1,X2,X3)
| ~ s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_53,plain,
( ext(X1,X2,X3,X4) = X1
| X1 = X2
| sameside(ext(X1,X2,X3,X4),X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_54,plain,
( s_t(X2,X3,X4)
| ~ s_t(X1,X2,X3)
| ~ s_t(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_55,plain,
! [X379,X380,X381] :
( ~ s_e(X379,X380,X381,X381)
| X379 = X380 ),
inference(variable_rename,[status(thm)],[c_0_43]) ).
fof(c_0_56,plain,
! [X12,X15,X14,X17] :
( ( ~ le(X12,X15,X14,X17)
| s_t(X12,X15,ins(X14,X17,X12,X15)) )
& ( ~ le(X12,X15,X14,X17)
| s_e(X12,ins(X14,X17,X12,X15),X14,X17) )
& ( ~ le(X12,X15,X14,X17)
| ins(X14,X17,X12,X15) = ext(X12,X15,insert(X12,X15,X14,X17),X17) ) ),
inference(fof_simplification,[status(thm)],[aSatz5_5a]) ).
cnf(c_0_57,plain,
( le(X1,X2,X3,X4)
| ~ s_t(X1,X2,X5)
| ~ s_e(X1,X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_58,plain,
! [X447,X448] : s_t(X447,X448,X448),
inference(variable_rename,[status(thm)],[aSatz3_1]) ).
cnf(c_0_59,plain,
( ext(X1,X2,X3,X2) = X3
| X1 = X2
| ~ s_t(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_60,plain,
( ext(X1,X2,X2,X3) = X3
| ~ s_t(X2,ext(X1,X2,X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_61,plain,
( s_t(X3,ext(ext(X4,X3,alpha,gamma),X3,X1,X2),X4)
| ~ le(X1,X2,X3,X4) ),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,plain,
le(X1,X2,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_63,plain,
! [X483,X484] : X483 != ext(X484,X483,alpha,gamma),
inference(variable_rename,[status(thm)],[aSatz3_14b]) ).
fof(c_0_64,negated_conjecture,
~ ! [X27,X12,X15,X14] :
( ( X27 = X12
| X15 = X14
| sameside(insert(X15,X14,X12,X27),X12,X27) )
& ( X27 = X12
| X15 = X14
| s_e(X12,insert(X15,X14,X12,X27),X15,X14) ) ),
inference(assume_negation,[status(cth)],[aSatz6_11a]) ).
fof(c_0_65,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_66,plain,
! [X12,X15,X14] :
( ~ s_t(X12,X15,X14)
| s_t(X14,X15,X12) ),
inference(fof_simplification,[status(thm)],[aSatz3_2]) ).
cnf(c_0_67,plain,
( ext(X1,X2,X3,X4) = X1
| X1 = X2
| ~ s_t(ext(X1,X2,X3,X4),X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_68,plain,
( s_t(X1,X2,ext(X3,X2,X4,X5))
| ~ s_t(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_41]) ).
cnf(c_0_69,plain,
( X1 = X2
| ~ s_e(X1,X2,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_70,plain,
! [X579,X580,X581,X582] :
( ( ~ le(X579,X580,X581,X582)
| s_t(X579,X580,ins(X581,X582,X579,X580)) )
& ( ~ le(X579,X580,X581,X582)
| s_e(X579,ins(X581,X582,X579,X580),X581,X582) )
& ( ~ le(X579,X580,X581,X582)
| ins(X581,X582,X579,X580) = ext(X579,X580,insert(X579,X580,X581,X582),X582) ) ),
inference(variable_rename,[status(thm)],[c_0_56]) ).
fof(c_0_71,plain,
! [X12,X15,X14,X17,X20,X21,X22,X26] :
( ~ le(X12,X15,X14,X17)
| ~ s_e(X12,X15,X20,X21)
| ~ s_e(X14,X17,X22,X26)
| le(X20,X21,X22,X26) ),
inference(fof_simplification,[status(thm)],[aSatz5_6]) ).
cnf(c_0_72,plain,
( le(X1,X2,X3,X4)
| ~ s_t(X1,X2,ext(X5,X1,X3,X4)) ),
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_73,plain,
s_t(X1,X2,X2),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_74,plain,
( ext(X1,X2,ext(X1,X2,X3,X4),X2) = ext(X1,X2,X3,X4)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_59,c_0_41]) ).
cnf(c_0_75,plain,
ext(ext(X1,X2,alpha,gamma),X2,X2,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_76,plain,
X1 != ext(X2,X1,alpha,gamma),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_77,negated_conjecture,
( ( esk1_0 != esk2_0
| esk1_0 != esk2_0 )
& ( esk3_0 != esk4_0
| esk1_0 != esk2_0 )
& ( ~ s_e(esk2_0,insert(esk3_0,esk4_0,esk2_0,esk1_0),esk3_0,esk4_0)
| esk1_0 != esk2_0 )
& ( esk1_0 != esk2_0
| esk3_0 != esk4_0 )
& ( esk3_0 != esk4_0
| esk3_0 != esk4_0 )
& ( ~ s_e(esk2_0,insert(esk3_0,esk4_0,esk2_0,esk1_0),esk3_0,esk4_0)
| esk3_0 != esk4_0 )
& ( esk1_0 != esk2_0
| ~ sameside(insert(esk3_0,esk4_0,esk2_0,esk1_0),esk2_0,esk1_0) )
& ( esk3_0 != esk4_0
| ~ sameside(insert(esk3_0,esk4_0,esk2_0,esk1_0),esk2_0,esk1_0) )
& ( ~ s_e(esk2_0,insert(esk3_0,esk4_0,esk2_0,esk1_0),esk3_0,esk4_0)
| ~ sameside(insert(esk3_0,esk4_0,esk2_0,esk1_0),esk2_0,esk1_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])]) ).
fof(c_0_78,plain,
! [X627,X628,X629,X630] :
( X627 = X628
| X629 = X628
| X630 = X628
| ~ s_t(X627,X628,X630)
| ~ s_t(X629,X628,X630)
| sameside(X627,X628,X629) ),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_79,plain,
! [X449,X450,X451] :
( ~ s_t(X449,X450,X451)
| s_t(X451,X450,X449) ),
inference(variable_rename,[status(thm)],[c_0_66]) ).
cnf(c_0_80,plain,
( ext(X1,ext(X2,X1,X3,X4),X5,X6) = X1
| ext(X2,X1,X3,X4) = X1
| ~ s_t(X2,ext(X1,ext(X2,X1,X3,X4),X5,X6),X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_81,plain,
ext(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_69,c_0_36]) ).
cnf(c_0_82,plain,
( ins(X3,X4,X1,X2) = ext(X1,X2,insert(X1,X2,X3,X4),X4)
| ~ le(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_83,plain,
! [X588,X589,X590,X591,X592,X593,X594,X595] :
( ~ le(X588,X589,X590,X591)
| ~ s_e(X588,X589,X592,X593)
| ~ s_e(X590,X591,X594,X595)
| le(X592,X593,X594,X595) ),
inference(variable_rename,[status(thm)],[c_0_71]) ).
cnf(c_0_84,plain,
le(X1,ext(X2,X1,X3,X4),X3,X4),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_85,plain,
ext(ext(X1,X2,alpha,gamma),X2,X1,X2) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_86,negated_conjecture,
( ~ s_e(esk2_0,insert(esk3_0,esk4_0,esk2_0,esk1_0),esk3_0,esk4_0)
| ~ sameside(insert(esk3_0,esk4_0,esk2_0,esk1_0),esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_87,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_78]) ).
cnf(c_0_88,plain,
( s_t(X3,X2,X1)
| ~ s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
( ext(X1,X2,X3,X4) = X2
| ~ s_t(X1,ext(X1,X2,X3,X4),X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,plain,
( ins(X3,X4,X1,X2) = ext(X1,X2,ext(ext(X4,X3,alpha,gamma),X3,X1,X2),X4)
| ~ le(X1,X2,X3,X4) ),
inference(rw,[status(thm)],[c_0_82,c_0_50]) ).
cnf(c_0_91,plain,
( s_e(X1,ins(X3,X4,X1,X2),X3,X4)
| ~ le(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_92,plain,
! [X452,X453] : s_t(X452,X452,X453),
inference(variable_rename,[status(thm)],[aSatz3_3]) ).
cnf(c_0_93,plain,
( le(X5,X6,X7,X8)
| ~ le(X1,X2,X3,X4)
| ~ s_e(X1,X2,X5,X6)
| ~ s_e(X3,X4,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_94,plain,
le(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_95,negated_conjecture,
( ~ sameside(ext(ext(esk1_0,esk2_0,alpha,gamma),esk2_0,esk3_0,esk4_0),esk2_0,esk1_0)
| ~ s_e(esk2_0,ext(ext(esk1_0,esk2_0,alpha,gamma),esk2_0,esk3_0,esk4_0),esk3_0,esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_50]),c_0_50]) ).
cnf(c_0_96,plain,
( ext(X1,X2,X3,X4) = X2
| X5 = X2
| X2 = X1
| sameside(X5,X2,X1)
| ~ s_t(X5,X2,ext(X1,X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_87,c_0_41]) ).
cnf(c_0_97,plain,
s_t(ext(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_88,c_0_41]) ).
cnf(c_0_98,negated_conjecture,
( esk1_0 != esk2_0
| esk1_0 != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_99,plain,
( ins(X1,X2,X3,X4) = X4
| ~ le(X3,X4,X1,X2)
| ~ s_t(X3,ins(X1,X2,X3,X4),X4) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_100,plain,
( ins(X1,X1,X2,X3) = X2
| ~ le(X2,X3,X1,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_91]) ).
cnf(c_0_101,plain,
s_t(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
( le(X1,X2,X3,X4)
| ~ s_e(X5,X6,X3,X4)
| ~ s_e(X6,X5,X1,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_103,negated_conjecture,
~ sameside(ext(ext(esk1_0,esk2_0,alpha,gamma),esk2_0,esk3_0,esk4_0),esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_36])]) ).
cnf(c_0_104,plain,
( ext(ext(X1,X2,X3,X4),X2,X5,X6) = X2
| ext(X1,X2,X3,X4) = X2
| X2 = X1
| sameside(ext(ext(X1,X2,X3,X4),X2,X5,X6),X2,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_105,negated_conjecture,
esk2_0 != esk1_0,
inference(cn,[status(thm)],[c_0_98]) ).
cnf(c_0_106,plain,
( X1 = X2
| ~ le(X1,X2,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101])]) ).
cnf(c_0_107,plain,
( le(X1,X2,X3,X4)
| ~ s_e(X3,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_102,c_0_46]) ).
cnf(c_0_108,negated_conjecture,
ext(ext(esk1_0,esk2_0,alpha,gamma),esk2_0,esk3_0,esk4_0) = esk2_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_76]),c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( esk3_0 != esk4_0
| esk3_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_110,plain,
( X1 = X2
| ~ s_e(X3,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,negated_conjecture,
s_e(esk2_0,esk2_0,esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_36,c_0_108]) ).
cnf(c_0_112,negated_conjecture,
esk4_0 != esk3_0,
inference(cn,[status(thm)],[c_0_109]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO497+1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % 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
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 4 17:59:51 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 147.78/107.13 % Version : CSE_E---1.7
% 147.78/107.13 % Problem : theBenchmark.p
% 147.78/107.13 % SZS status Theorem for theBenchmark.p
% 147.78/107.13 % SZS output start CNFRefutation
% See solution above
% 148.15/107.51 % Total time : 93.496s
%------------------------------------------------------------------------------