%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KRS084+1 : TPTP v9.2.1. Released v3.1.0.
% 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 : 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 04:36:18 PM UTC 2026
% Result : Unsatisfiable 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 4 unt; 0 def)
% Number of atoms : 128 ( 5 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 156 ( 65 ~; 57 |; 24 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 71 ( 1 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_3,axiom,
! [X4] :
( cd(X4)
<=> ( ? [X5] :
( rf(X4,X5)
& ~ cc(X5) )
& cc(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(axiom_2,axiom,
! [X4] :
( cUnsatisfiable(X4)
<=> ( ? [X5] :
( rinvF(X4,X5)
& cd(X5) )
& ! [X5] :
( rinvR(X4,X5)
=> ? [X6] :
( rinvF(X5,X6)
& cd(X6) ) )
& ~ cc(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(axiom_4,axiom,
! [X4,X5,X6] :
( ( rf(X4,X5)
& rf(X4,X6) )
=> X5 = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X4,X5] :
( rinvF(X4,X5)
<=> rf(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X4,X5] :
( rinvR(X4,X5)
<=> rr(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(axiom_9,axiom,
! [X4,X5] :
( rf(X4,X5)
=> rr(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_19_35232),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(c_0_7,plain,
! [X4] :
( cd(X4)
<=> ( ? [X5] :
( rf(X4,X5)
& ~ cc(X5) )
& cc(X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
fof(c_0_8,plain,
! [X4] :
( cUnsatisfiable(X4)
<=> ( ? [X5] :
( rinvF(X4,X5)
& cd(X5) )
& ! [X5] :
( rinvR(X4,X5)
=> ? [X6] :
( rinvF(X5,X6)
& cd(X6) ) )
& ~ cc(X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_9,plain,
! [X117,X118,X119] :
( ~ rf(X117,X118)
| ~ rf(X117,X119)
| X118 = X119 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])]) ).
fof(c_0_10,plain,
! [X113,X115,X116] :
( ( rf(X113,esk4_1(X113))
| ~ cd(X113) )
& ( ~ cc(esk4_1(X113))
| ~ cd(X113) )
& ( cc(X113)
| ~ cd(X113) )
& ( ~ rf(X115,X116)
| cc(X116)
| ~ cc(X115)
| cd(X115) ) ),
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)],[c_0_7])])])])])]) ).
fof(c_0_11,plain,
! [X120,X121] :
( ( ~ rinvF(X120,X121)
| rf(X121,X120) )
& ( ~ rf(X121,X120)
| rinvF(X120,X121) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])]) ).
fof(c_0_12,plain,
! [X105,X107,X109,X110,X112] :
( ( rinvF(X105,esk1_1(X105))
| ~ cUnsatisfiable(X105) )
& ( cd(esk1_1(X105))
| ~ cUnsatisfiable(X105) )
& ( rinvF(X107,esk2_2(X105,X107))
| ~ rinvR(X105,X107)
| ~ cUnsatisfiable(X105) )
& ( cd(esk2_2(X105,X107))
| ~ rinvR(X105,X107)
| ~ cUnsatisfiable(X105) )
& ( ~ cc(X105)
| ~ cUnsatisfiable(X105) )
& ( rinvR(X109,esk3_1(X109))
| ~ rinvF(X109,X110)
| ~ cd(X110)
| cc(X109)
| cUnsatisfiable(X109) )
& ( ~ rinvF(esk3_1(X109),X112)
| ~ cd(X112)
| ~ rinvF(X109,X110)
| ~ cd(X110)
| cc(X109)
| cUnsatisfiable(X109) ) ),
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)],[c_0_8])])])])])]) ).
cnf(c_0_13,plain,
( X2 = X3
| ~ rf(X1,X2)
| ~ rf(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( rf(X1,esk4_1(X1))
| ~ cd(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( rf(X2,X1)
| ~ rinvF(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( rinvF(X1,esk2_2(X2,X1))
| ~ rinvR(X2,X1)
| ~ cUnsatisfiable(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X1 = esk4_1(X2)
| ~ rf(X2,X1)
| ~ cd(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( rf(esk2_2(X1,X2),X2)
| ~ rinvR(X1,X2)
| ~ cUnsatisfiable(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( cd(esk2_2(X1,X2))
| ~ rinvR(X1,X2)
| ~ cUnsatisfiable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ cc(esk4_1(X1))
| ~ cd(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
( esk4_1(esk2_2(X1,X2)) = X2
| ~ rinvR(X1,X2)
| ~ cUnsatisfiable(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
fof(c_0_22,plain,
! [X122,X123] :
( ( ~ rinvR(X122,X123)
| rr(X123,X122) )
& ( ~ rr(X123,X122)
| rinvR(X122,X123) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_6])]) ).
cnf(c_0_23,plain,
( ~ rinvR(X1,X2)
| ~ cc(X2)
| ~ cUnsatisfiable(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_24,plain,
( rinvR(X2,X1)
| ~ rr(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X127,X128] :
( ~ rf(X127,X128)
| rr(X127,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_9])]) ).
cnf(c_0_26,plain,
( ~ rr(X1,X2)
| ~ cc(X1)
| ~ cUnsatisfiable(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( rr(X1,X2)
| ~ rf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,plain,
( rinvF(X1,esk1_1(X1))
| ~ cUnsatisfiable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,plain,
( ~ rf(X1,X2)
| ~ cc(X1)
| ~ cUnsatisfiable(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
( rf(esk1_1(X1),X1)
| ~ cUnsatisfiable(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_31,plain,
( ~ cc(esk1_1(X1))
| ~ cUnsatisfiable(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
( cc(X1)
| ~ cd(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,plain,
( cd(esk1_1(X1))
| ~ cUnsatisfiable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,plain,
cUnsatisfiable(i2003_11_14_17_19_35232),
inference(split_conjunct,[status(thm)],[axiom_8]) ).
cnf(c_0_35,plain,
~ cUnsatisfiable(X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[c_0_34,c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS084+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n019.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:36:59 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------