%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KRS109+1 : TPTP v9.2.1. Released v3.1.0.
% 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 : n005.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 04:36:22 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 127 ( 5 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 133 ( 52 ~; 51 |; 19 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 68 ( 1 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X4] :
( cUnsatisfiable(X4)
<=> ( cpxcomp(X4)
& ? [X5] :
( rf(X4,X5)
& ca_Ax2(X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(axiom_9,axiom,
! [X4,X5] :
( rinvF(X4,X5)
<=> rf(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(axiom_13,axiom,
cUnsatisfiable(i2003_11_14_17_21_08508),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
fof(axiom_5,axiom,
! [X4] :
( ca_Ax2(X4)
<=> ( ! [X5] :
( rinvS(X4,X5)
=> cp(X5) )
& ! [X5] :
( rinvF(X4,X5)
=> ca_Vx3(X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X4] :
( ca_Vx3(X4)
<=> ? [X5] :
( rs(X4,X5)
& cp(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X4,X5,X7] :
( ( rf(X4,X5)
& rf(X4,X7) )
=> X5 = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(axiom_14,axiom,
! [X4,X5] :
( rs(X4,X5)
=> rf(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(axiom_3,axiom,
! [X4] :
( cp(X4)
<=> ~ ? [X5] : ra_Px1(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X4] :
( cpxcomp(X4)
<=> ? [X6] : ra_Px1(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(axiom_11,axiom,
! [X4,X5] :
( rinvS(X4,X5)
<=> rs(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(c_0_10,plain,
! [X162,X164,X165] :
( ( cpxcomp(X162)
| ~ cUnsatisfiable(X162) )
& ( rf(X162,esk1_1(X162))
| ~ cUnsatisfiable(X162) )
& ( ca_Ax2(esk1_1(X162))
| ~ cUnsatisfiable(X162) )
& ( ~ cpxcomp(X164)
| ~ rf(X164,X165)
| ~ ca_Ax2(X165)
| cUnsatisfiable(X164) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_2])])])])])]) ).
fof(c_0_11,plain,
! [X190,X191] :
( ( ~ rinvF(X190,X191)
| rf(X191,X190) )
& ( ~ rf(X191,X190)
| rinvF(X190,X191) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_9])]) ).
cnf(c_0_12,plain,
( rf(X1,esk1_1(X1))
| ~ cUnsatisfiable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
cUnsatisfiable(i2003_11_14_17_21_08508),
inference(split_conjunct,[status(thm)],[axiom_13]) ).
fof(c_0_14,plain,
! [X174,X175,X176,X177] :
( ( ~ rinvS(X174,X175)
| cp(X175)
| ~ ca_Ax2(X174) )
& ( ~ rinvF(X174,X176)
| ca_Vx3(X176)
| ~ ca_Ax2(X174) )
& ( rinvF(X177,esk5_1(X177))
| rinvS(X177,esk4_1(X177))
| ca_Ax2(X177) )
& ( ~ ca_Vx3(esk5_1(X177))
| rinvS(X177,esk4_1(X177))
| ca_Ax2(X177) )
& ( rinvF(X177,esk5_1(X177))
| ~ cp(esk4_1(X177))
| ca_Ax2(X177) )
& ( ~ ca_Vx3(esk5_1(X177))
| ~ cp(esk4_1(X177))
| ca_Ax2(X177) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])])]) ).
cnf(c_0_15,plain,
( rinvF(X2,X1)
| ~ rf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
rf(i2003_11_14_17_21_08508,esk1_1(i2003_11_14_17_21_08508)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ca_Ax2(esk1_1(X1))
| ~ cUnsatisfiable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,plain,
! [X180,X182,X183] :
( ( rs(X180,esk6_1(X180))
| ~ ca_Vx3(X180) )
& ( cp(esk6_1(X180))
| ~ ca_Vx3(X180) )
& ( ~ rs(X182,X183)
| ~ cp(X183)
| ca_Vx3(X182) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_6])])])])])]) ).
cnf(c_0_19,plain,
( ca_Vx3(X2)
| ~ rinvF(X1,X2)
| ~ ca_Ax2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
rinvF(esk1_1(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
ca_Ax2(esk1_1(i2003_11_14_17_21_08508)),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
fof(c_0_22,plain,
! [X184,X185,X186] :
( ~ rf(X184,X185)
| ~ rf(X184,X186)
| X185 = X186 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_7])]) ).
fof(c_0_23,plain,
! [X199,X200] :
( ~ rs(X199,X200)
| rf(X199,X200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_14])]) ).
cnf(c_0_24,plain,
( rs(X1,esk6_1(X1))
| ~ ca_Vx3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
ca_Vx3(i2003_11_14_17_21_08508),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
( X2 = X3
| ~ rf(X1,X2)
| ~ rf(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( rf(X1,X2)
| ~ rs(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
rs(i2003_11_14_17_21_08508,esk6_1(i2003_11_14_17_21_08508)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_29,plain,
! [X166,X167,X168] :
( ( ~ cp(X166)
| ~ ra_Px1(X166,X167) )
& ( ra_Px1(X168,esk2_1(X168))
| cp(X168) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_3])])])])]) ).
fof(c_0_30,plain,
! [X170,X172,X173] :
( ( ~ cpxcomp(X170)
| ra_Px1(X170,esk3_1(X170)) )
& ( ~ ra_Px1(X172,X173)
| cpxcomp(X172) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])])])])]) ).
cnf(c_0_31,plain,
( X1 = esk1_1(i2003_11_14_17_21_08508)
| ~ rf(i2003_11_14_17_21_08508,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_32,plain,
rf(i2003_11_14_17_21_08508,esk6_1(i2003_11_14_17_21_08508)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( ~ cp(X1)
| ~ ra_Px1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
( ra_Px1(X1,esk3_1(X1))
| ~ cpxcomp(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,plain,
! [X194,X195] :
( ( ~ rinvS(X194,X195)
| rs(X195,X194) )
& ( ~ rs(X195,X194)
| rinvS(X194,X195) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_11])]) ).
cnf(c_0_36,plain,
esk6_1(i2003_11_14_17_21_08508) = esk1_1(i2003_11_14_17_21_08508),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( ~ cpxcomp(X1)
| ~ cp(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( cpxcomp(X1)
| ~ cUnsatisfiable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_39,plain,
( rinvS(X2,X1)
| ~ rs(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
rs(i2003_11_14_17_21_08508,esk1_1(i2003_11_14_17_21_08508)),
inference(rw,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_41,plain,
( ~ cp(X1)
| ~ cUnsatisfiable(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( cp(X2)
| ~ rinvS(X1,X2)
| ~ ca_Ax2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,plain,
rinvS(esk1_1(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
~ cp(i2003_11_14_17_21_08508),
inference(spm,[status(thm)],[c_0_41,c_0_13]) ).
cnf(c_0_45,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_21])]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS109+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 20:37:15 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------