%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC085+1 : TPTP v9.2.1. Released v2.4.0.
% 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 05:18:12 PM UTC 2026
% Result : Theorem 1.49s 1.78s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 14 unt; 0 def)
% Number of atoms : 178 ( 36 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 213 ( 83 ~; 84 |; 27 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 30 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ frontsegP(X4,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ frontsegP(X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_9,plain,
! [X236,X237,X240,X241] :
( ( ssList(esk8_2(X236,X237))
| ~ segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) )
& ( ssList(esk9_2(X236,X237))
| ~ segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) )
& ( app(app(esk8_2(X236,X237),X237),esk9_2(X236,X237)) = X236
| ~ segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) )
& ( ~ ssList(X240)
| ~ ssList(X241)
| app(app(X240,X237),X241) != X236
| segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X463] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ( ~ ssList(X463)
| ~ neq(X463,nil)
| ~ segmentP(esk49_0,X463)
| ~ segmentP(esk48_0,X463) )
& ( neq(esk50_0,nil)
| nil = esk51_0 )
& ( frontsegP(esk51_0,esk50_0)
| nil = esk51_0 )
& ( neq(esk50_0,nil)
| nil = esk50_0 )
& ( frontsegP(esk51_0,esk50_0)
| nil = esk50_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_11,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X343] :
( ~ ssList(X343)
| app(nil,X343) = X343 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_13,plain,
! [X338,X339] :
( ~ ssList(X338)
| ~ ssList(X339)
| ssList(app(X338,X339)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_14,plain,
! [X228,X229,X231] :
( ( ssList(esk6_2(X228,X229))
| ~ frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( app(X229,esk6_2(X228,X229)) = X228
| ~ frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( ~ ssList(X231)
| app(X229,X231) != X228
| frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_20,plain,
! [X397] :
( ~ ssList(X397)
| segmentP(X397,X397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_21,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_24,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( frontsegP(esk51_0,esk50_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_29,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_30,plain,
! [X402] :
( ~ ssList(X402)
| segmentP(X402,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_31,negated_conjecture,
( ~ segmentP(esk50_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_18]),c_0_16]) ).
cnf(c_0_32,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_34,negated_conjecture,
( app(esk50_0,esk6_2(esk51_0,esk50_0)) = esk51_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_35,negated_conjecture,
( esk50_0 = nil
| ssList(esk6_2(esk51_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_28]),c_0_27])]) ).
cnf(c_0_36,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28])]) ).
cnf(c_0_38,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_28])]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( neq(esk50_0,nil)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,negated_conjecture,
( ~ segmentP(esk51_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_36]),c_0_23]),c_0_28])]) ).
cnf(c_0_41,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_42,negated_conjecture,
( neq(esk50_0,nil)
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_43,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_27])]) ).
cnf(c_0_45,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_41,c_0_16]) ).
cnf(c_0_46,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC085+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : Tue May 5 04:23:45 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.49/1.78 % Version : CSE_E---1.7
% 1.49/1.78 % Problem : theBenchmark.p
% 1.49/1.78 % SZS status Theorem for theBenchmark.p
% 1.49/1.78 % SZS output start CNFRefutation
% See solution above
% 1.49/1.79 % Total time : 1.372s
%------------------------------------------------------------------------------