%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO526+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 : n010.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 04:21:27 PM UTC 2026
% Result : Theorem 181.48s 143.70s
% Output : CNFRefutation 181.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 127 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 137 ( 65 ~; 63 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz10_12c,conjecture,
! [X12,X15,X14,X20,X22] :
( ~ s_r(X12,X15,X14)
| ~ s_r(X20,X15,X22)
| ~ s_e(X12,X15,X20,X15)
| ~ s_e(X15,X14,X15,X22)
| s_e(X12,X14,X20,X22)
| X15 != midpoint(X14,X22)
| X14 = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12c) ).
fof(aSatz7_6,axiom,
! [X13,X12,X16] :
( ~ s_m(X13,X12,X16)
| X16 = s(X12,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_6) ).
fof(aSatz8_22,axiom,
! [X12,X15] : s_m(X12,midpoint(X12,X15),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22) ).
fof(aSatz8_4,axiom,
! [X12,X15,X14] :
( ~ s_r(X12,X15,X14)
| s_r(X12,X15,s(X15,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_4) ).
fof(aSatz8_2,axiom,
! [X12,X15,X14] :
( ~ s_r(X12,X15,X14)
| s_r(X14,X15,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_2) ).
fof(aSatz2_3,axiom,
! [X12,X15,X14,X17,X18,X19] :
( ~ s_e(X12,X15,X14,X17)
| ~ s_e(X14,X17,X18,X19)
| s_e(X12,X15,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_3) ).
fof(d_Defn8_1,axiom,
! [X12,X15,X14] :
( ( ~ s_r(X12,X15,X14)
| s_e(X12,X14,X12,s(X15,X14)) )
& ( s_r(X12,X15,X14)
| ~ s_e(X12,X14,X12,s(X15,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_1) ).
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(aSatz7_7,axiom,
! [X12,X13] : s(X12,s(X12,X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_7) ).
fof(aSatz10_12b,axiom,
! [X12,X15,X14,X20] :
( ~ s_r(X12,X15,X14)
| ~ s_r(X20,X15,X14)
| ~ s_e(X12,X15,X20,X15)
| s_e(X12,X14,X20,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12b) ).
fof(c_0_10,negated_conjecture,
~ ! [X12,X15,X14,X20,X22] :
( ~ s_r(X12,X15,X14)
| ~ s_r(X20,X15,X22)
| ~ s_e(X12,X15,X20,X15)
| ~ s_e(X15,X14,X15,X22)
| s_e(X12,X14,X20,X22)
| X15 != midpoint(X14,X22)
| X14 = X22 ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[aSatz10_12c])]) ).
fof(c_0_11,plain,
! [X13,X12,X16] :
( ~ s_m(X13,X12,X16)
| X16 = s(X12,X13) ),
inference(fof_simplification,[status(thm)],[aSatz7_6]) ).
fof(c_0_12,plain,
! [X1490,X1491] : s_m(X1490,midpoint(X1490,X1491),X1491),
inference(variable_rename,[status(thm)],[aSatz8_22]) ).
fof(c_0_13,negated_conjecture,
( s_r(esk1_0,esk2_0,esk3_0)
& s_r(esk4_0,esk2_0,esk5_0)
& s_e(esk1_0,esk2_0,esk4_0,esk2_0)
& s_e(esk2_0,esk3_0,esk2_0,esk5_0)
& ~ s_e(esk1_0,esk3_0,esk4_0,esk5_0)
& esk2_0 = midpoint(esk3_0,esk5_0)
& esk3_0 != esk5_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,plain,
! [X12,X15,X14] :
( ~ s_r(X12,X15,X14)
| s_r(X12,X15,s(X15,X14)) ),
inference(fof_simplification,[status(thm)],[aSatz8_4]) ).
fof(c_0_15,plain,
! [X1296,X1297,X1298] :
( ~ s_m(X1296,X1297,X1298)
| X1298 = s(X1297,X1296) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
s_m(X1,midpoint(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
esk2_0 = midpoint(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X12,X15,X14] :
( ~ s_r(X12,X15,X14)
| s_r(X14,X15,X12) ),
inference(fof_simplification,[status(thm)],[aSatz8_2]) ).
fof(c_0_19,plain,
! [X1382,X1383,X1384] :
( ~ s_r(X1382,X1383,X1384)
| s_r(X1382,X1383,s(X1383,X1384)) ),
inference(variable_rename,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( X3 = s(X2,X1)
| ~ s_m(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
s_m(esk3_0,esk2_0,esk5_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X12,X15,X14,X17,X18,X19] :
( ~ s_e(X12,X15,X14,X17)
| ~ s_e(X14,X17,X18,X19)
| s_e(X12,X15,X18,X19) ),
inference(fof_simplification,[status(thm)],[aSatz2_3]) ).
fof(c_0_23,plain,
! [X12,X15,X14] :
( ( ~ s_r(X12,X15,X14)
| s_e(X12,X14,X12,s(X15,X14)) )
& ( s_r(X12,X15,X14)
| ~ s_e(X12,X14,X12,s(X15,X14)) ) ),
inference(fof_simplification,[status(thm)],[d_Defn8_1]) ).
fof(c_0_24,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_25,plain,
! [X1375,X1376,X1377] :
( ~ s_r(X1375,X1376,X1377)
| s_r(X1377,X1376,X1375) ),
inference(variable_rename,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( s_r(X1,X2,s(X2,X3))
| ~ s_r(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
s(esk2_0,esk3_0) = esk5_0,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,plain,
! [X968,X969,X970,X971,X972,X973] :
( ~ s_e(X968,X969,X970,X971)
| ~ s_e(X970,X971,X972,X973)
| s_e(X968,X969,X972,X973) ),
inference(variable_rename,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X1790,X1791,X1792] :
( ( ~ s_r(X1790,X1791,X1792)
| s_e(X1790,X1792,X1790,s(X1791,X1792)) )
& ( s_r(X1790,X1791,X1792)
| ~ s_e(X1790,X1792,X1790,s(X1791,X1792)) ) ),
inference(variable_rename,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X1299,X1300] : s(X1299,s(X1299,X1300)) = X1300,
inference(variable_rename,[status(thm)],[aSatz7_7]) ).
fof(c_0_31,plain,
! [X12,X15,X14,X20] :
( ~ s_r(X12,X15,X14)
| ~ s_r(X20,X15,X14)
| ~ s_e(X12,X15,X20,X15)
| s_e(X12,X14,X20,X14) ),
inference(fof_simplification,[status(thm)],[aSatz10_12b]) ).
fof(c_0_32,plain,
! [X964,X965,X966,X967] :
( ~ s_e(X964,X965,X966,X967)
| s_e(X966,X967,X964,X965) ),
inference(variable_rename,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( s_r(X3,X2,X1)
| ~ s_r(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( s_r(X1,esk2_0,esk5_0)
| ~ s_r(X1,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( s_e(X1,X2,X5,X6)
| ~ s_e(X1,X2,X3,X4)
| ~ s_e(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( s_e(X1,X3,X1,s(X2,X3))
| ~ s_r(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
s(X1,s(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_38,plain,
! [X1726,X1727,X1728,X1729] :
( ~ s_r(X1726,X1727,X1728)
| ~ s_r(X1729,X1727,X1728)
| ~ s_e(X1726,X1727,X1729,X1727)
| s_e(X1726,X1728,X1729,X1728) ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( s_e(X3,X4,X1,X2)
| ~ s_e(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
s_e(esk1_0,esk2_0,esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,negated_conjecture,
( s_r(esk5_0,esk2_0,X1)
| ~ s_r(X1,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
s_r(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_43,plain,
( s_e(X1,X2,X3,s(X4,X5))
| ~ s_r(X3,X4,X5)
| ~ s_e(X1,X2,X3,X5) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
s(esk2_0,esk5_0) = esk3_0,
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_45,plain,
( s_e(X1,X3,X4,X3)
| ~ s_r(X1,X2,X3)
| ~ s_r(X4,X2,X3)
| ~ s_e(X1,X2,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
s_e(esk4_0,esk2_0,esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
s_r(esk5_0,esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( s_e(X1,X2,X3,esk3_0)
| ~ s_r(X3,esk2_0,esk5_0)
| ~ s_e(X1,X2,X3,esk5_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( s_e(esk4_0,X1,esk1_0,X1)
| ~ s_r(esk1_0,esk2_0,X1)
| ~ s_r(esk4_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
s_r(esk1_0,esk2_0,esk5_0),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
s_r(esk4_0,esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_52,negated_conjecture,
s_e(esk4_0,esk5_0,esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_53,negated_conjecture,
~ s_e(esk1_0,esk3_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO526+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
% 0.15/0.32 % Computer : n010.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 18:01:21 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 181.48/143.70 % Version : CSE_E---1.7
% 181.48/143.70 % Problem : theBenchmark.p
% 181.48/143.70 % SZS status Theorem for theBenchmark.p
% 181.48/143.70 % SZS output start CNFRefutation
% See solution above
% 181.67/143.98 % Total time : 133.619s
%------------------------------------------------------------------------------