%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC248+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:00 PM UTC 2026
% Result : Theorem 259.11s 38.89s
% Output : CNFRefutation 259.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 104 ( 17 unt; 0 def)
% Number of atoms : 418 ( 164 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 527 ( 213 ~; 218 |; 78 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 191 ( 0 sgn 156 !; 35 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssList(X8)
=> ! [X9] :
( ? [X14] :
( ? [X15] :
( ? [X16] :
( ? [X17] :
( leq(X16,X14)
& app(X17,cons(X16,nil)) = X2
& ssList(X17) )
& ssItem(X16) )
& app(cons(X14,nil),X15) = X9
& ssList(X15) )
& ssItem(X14) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X10,X12)
& app(cons(X12,nil),X13) = X2
& ssList(X13) )
& ssItem(X12) )
& app(X11,cons(X10,nil)) = X8
& ssList(X11) )
& ssItem(X10) )
| ~ totalorderedP(X2)
| app(app(X8,X2),X9) != X3
| ~ ssList(X9) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssList(X8)
=> ! [X9] :
( ? [X14] :
( ? [X15] :
( ? [X16] :
( ? [X17] :
( leq(X16,X14)
& app(X17,cons(X16,nil)) = X2
& ssList(X17) )
& ssItem(X16) )
& app(cons(X14,nil),X15) = X9
& ssList(X15) )
& ssItem(X14) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X10,X12)
& app(cons(X12,nil),X13) = X2
& ssList(X13) )
& ssItem(X12) )
& app(X11,cons(X10,nil)) = X8
& ssList(X11) )
& ssItem(X10) )
| ~ totalorderedP(X2)
| app(app(X8,X2),X9) != X3
| ~ ssList(X9) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(flattening,[],[f123]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ! [X14] :
( ! [X15] :
( ! [X16] :
( ! [X17] :
( ~ leq(X16,X14)
| app(X17,cons(X16,nil)) != X2
| ~ ssList(X17) )
| ~ ssItem(X16) )
| app(cons(X14,nil),X15) != X9
| ~ ssList(X15) )
| ~ ssItem(X14) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X8
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X8,X2),X9) = X3
& ssList(X9) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ( cons(sK50(X0),sK49(X0)) = X0
& ssItem(sK50(X0))
& ssList(sK49(X0)) )
| nil = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50]),skolemize(X1,sK49(X0)),skolemize(X2,sK50(X0))],[f124]) ).
fof(f295,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ( nil != sK55
| nil = sK56 )
& ssList(sK58)
& ! [X14] :
( ! [X15] :
( ! [X16] :
( ! [X17] :
( ~ leq(X16,X14)
| app(X17,cons(X16,nil)) != sK55
| ~ ssList(X17) )
| ~ ssItem(X16) )
| app(cons(X14,nil),X15) != sK59
| ~ ssList(X15) )
| ~ ssItem(X14) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK58
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& sK56 = app(app(sK58,sK55),sK59)
& ssList(sK59)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ leq(X4,sK57(X4,X5,X6))
& lt(X4,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& memberP(X5,sK57(X4,X5,X6))
& ssItem(sK57(X4,X5,X6)) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK53
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6)),skolemize(X8,sK58),skolemize(X9,sK59)],[f221]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f392,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK50(X0),sK49(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f273]) ).
fof(f393,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK50(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f273]) ).
fof(f394,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK49(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f273]) ).
fof(f400,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f418,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f476,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f481,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
! [X6,X4,X5] :
( memberP(X5,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f295]) ).
fof(f509,plain,
! [X6,X4,X5] :
( ssItem(sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
nil != sK53,
inference(cnf_transformation,[],[f295]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f514,plain,
nil != sK55,
inference(definition_unfolding,[],[f510,f511]) ).
fof(f515,plain,
! [X6,X4,X5] :
( ssItem(sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f509,f511]) ).
fof(f516,plain,
! [X6,X4,X5] :
( memberP(X5,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f508,f511]) ).
fof(f521,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f511]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f388]) ).
tcf(c_145,plain,
! [X0: $i] :
( ssList(sK49(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f394]) ).
tcf(c_146,plain,
! [X0: $i] :
( ssItem(sK50(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_147,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(sK50(X0),sK49(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f392]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f400]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f418]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f476]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f481]) ).
tcf(c_247,negated_conjecture,
nil != sK55,
inference(cnf_transformation,[],[f514]) ).
tcf(c_248,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sK57(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_249,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X0,sK57(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_262,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f521]) ).
tcf(c_9128,negated_conjecture,
ssList(sK55),
inference(subtyping,[status(esa)],[c_262]) ).
tcf(c_9138,negated_conjecture,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1] :
( memberP(X0_iProver_sP4_1,sK57(X0_iProver_ssItem_1,X0_iProver_sP4_1,X1_iProver_sP4_1))
| ~ ssList(X1_iProver_sP4_1)
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ( app(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)),X1_iProver_sP4_1) != sK55 ) ),
inference(subtyping,[status(esa)],[c_249]) ).
tcf(c_9139,negated_conjecture,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1] :
( ssItem(sK57(X0_iProver_ssItem_1,X0_iProver_sP4_1,X1_iProver_sP4_1))
| ~ ssList(X1_iProver_sP4_1)
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1)
| ( app(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)),X1_iProver_sP4_1) != sK55 ) ),
inference(subtyping,[status(esa)],[c_248]) ).
tcf(c_9140,negated_conjecture,
nil != sK55,
inference(subtyping,[status(esa)],[c_247]) ).
tcf(c_9153,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( app(X0_iProver_sP4_1,nil) = X0_iProver_sP4_1 )
| ~ ssList(X0_iProver_sP4_1) ),
inference(subtyping,[status(esa)],[c_232]) ).
tcf(c_9157,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1] :
( ( app(cons(X0_iProver_ssItem_1,nil),X0_iProver_sP4_1) = cons(X0_iProver_ssItem_1,X0_iProver_sP4_1) )
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_227]) ).
tcf(c_9202,plain,
! [X0_iProver_ssItem_1: iProver_ssItem_1] :
( ~ ssItem(X0_iProver_ssItem_1)
| ~ memberP(nil,X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_171]) ).
tcf(c_9218,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( app(nil,X0_iProver_sP4_1) = X0_iProver_sP4_1 )
| ~ ssList(X0_iProver_sP4_1) ),
inference(subtyping,[status(esa)],[c_155]) ).
tcf(c_9220,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X1_iProver_sP4_1: iProver_sP4_1] :
( ssList(app(X0_iProver_sP4_1,X1_iProver_sP4_1))
| ~ ssList(X1_iProver_sP4_1)
| ~ ssList(X0_iProver_sP4_1) ),
inference(subtyping,[status(esa)],[c_153]) ).
tcf(c_9226,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( X0_iProver_sP4_1 = nil )
| ( cons(sK50(X0_iProver_sP4_1),sK49(X0_iProver_sP4_1)) = X0_iProver_sP4_1 )
| ~ ssList(X0_iProver_sP4_1) ),
inference(subtyping,[status(esa)],[c_147]) ).
tcf(c_9227,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ssItem(sK50(X0_iProver_sP4_1))
| ( X0_iProver_sP4_1 = nil )
| ~ ssList(X0_iProver_sP4_1) ),
inference(subtyping,[status(esa)],[c_146]) ).
tcf(c_9228,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ssList(sK49(X0_iProver_sP4_1))
| ( X0_iProver_sP4_1 = nil )
| ~ ssList(X0_iProver_sP4_1) ),
inference(subtyping,[status(esa)],[c_145]) ).
tcf(c_9233,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1] :
( ssList(cons(X0_iProver_ssItem_1,X0_iProver_sP4_1))
| ~ ssList(X0_iProver_sP4_1)
| ~ ssItem(X0_iProver_ssItem_1) ),
inference(subtyping,[status(esa)],[c_140]) ).
tcf(c_9311,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] : X0_iProver_sP4_1 = X0_iProver_sP4_1,
theory(equality) ).
tcf(c_9313,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X1_iProver_sP4_1: iProver_sP4_1,X2_iProver_sP4_1: iProver_sP4_1] :
( ( X2_iProver_sP4_1 = X0_iProver_sP4_1 )
| ( X2_iProver_sP4_1 != X1_iProver_sP4_1 )
| ( X0_iProver_sP4_1 != X1_iProver_sP4_1 ) ),
theory(equality) ).
tcf(c_9317,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X1_iProver_sP4_1: iProver_sP4_1,X2_iProver_sP4_1: iProver_sP4_1,X3_iProver_sP4_1: iProver_sP4_1] :
( ( app(X0_iProver_sP4_1,X2_iProver_sP4_1) = app(X1_iProver_sP4_1,X3_iProver_sP4_1) )
| ( X2_iProver_sP4_1 != X3_iProver_sP4_1 )
| ( X0_iProver_sP4_1 != X1_iProver_sP4_1 ) ),
theory(equality) ).
tcf(c_9340,plain,
nil = nil,
inference(instantiation,[status(thm)],[c_9311]) ).
tcf(c_12378,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( nil = sK55 )
| ( sK55 != X0_iProver_sP4_1 )
| ( nil != X0_iProver_sP4_1 ) ),
inference(instantiation,[status(thm)],[c_9313]) ).
tcf(c_12379,plain,
( ( nil = sK55 )
| ( sK55 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_12378]) ).
tcf(c_12784,plain,
( ( sK55 = nil )
| ( cons(sK50(sK55),sK49(sK55)) = sK55 )
| ~ ssList(sK55) ),
inference(instantiation,[status(thm)],[c_9226]) ).
tcf(c_12789,plain,
( ssList(sK49(sK55))
| ( sK55 = nil )
| ~ ssList(sK55) ),
inference(instantiation,[status(thm)],[c_9228]) ).
tcf(c_12790,plain,
( ssItem(sK50(sK55))
| ( sK55 = nil )
| ~ ssList(sK55) ),
inference(instantiation,[status(thm)],[c_9227]) ).
tcf(c_14583,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1,X2_iProver_sP4_1: iProver_sP4_1] :
( ( X2_iProver_sP4_1 = cons(X0_iProver_ssItem_1,X0_iProver_sP4_1) )
| ( X2_iProver_sP4_1 != X1_iProver_sP4_1 )
| ( cons(X0_iProver_ssItem_1,X0_iProver_sP4_1) != X1_iProver_sP4_1 ) ),
inference(instantiation,[status(thm)],[c_9313]) ).
tcf(c_16277,plain,
sK55 = sK55,
inference(instantiation,[status(thm)],[c_9311]) ).
tcf(c_21767,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( X0_iProver_sP4_1 = cons(sK50(sK55),sK49(sK55)) )
| ( X0_iProver_sP4_1 != sK55 )
| ( cons(sK50(sK55),sK49(sK55)) != sK55 ) ),
inference(instantiation,[status(thm)],[c_14583]) ).
tcf(c_25928,plain,
( ( sK55 = cons(sK50(sK55),sK49(sK55)) )
| ( sK55 != sK55 )
| ( cons(sK50(sK55),sK49(sK55)) != sK55 ) ),
inference(instantiation,[status(thm)],[c_21767]) ).
tcf(c_48716,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( X0_iProver_sP4_1 = nil )
| ( app(sK49(X0_iProver_sP4_1),nil) = sK49(X0_iProver_sP4_1) )
| ~ ssList(X0_iProver_sP4_1) ),
inference(superposition,[status(thm)],[c_9228,c_9153]) ).
tcf(c_49768,plain,
( ( nil = sK55 )
| ( app(sK49(sK55),nil) = sK49(sK55) ) ),
inference(superposition,[status(thm)],[c_9128,c_48716]) ).
tcf(c_49801,plain,
app(sK49(sK55),nil) = sK49(sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_49768,c_9140]) ).
tcf(c_94076,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1,X2_iProver_sP4_1: iProver_sP4_1] :
( ( app(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)),X1_iProver_sP4_1) = sK55 )
| ( sK55 != X2_iProver_sP4_1 )
| ( app(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)),X1_iProver_sP4_1) != X2_iProver_sP4_1 ) ),
inference(instantiation,[status(thm)],[c_9313]) ).
tcf(c_94253,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X1_iProver_sP4_1: iProver_sP4_1] :
( ( sK55 = X0_iProver_sP4_1 )
| ( sK55 != X1_iProver_sP4_1 )
| ( X0_iProver_sP4_1 != X1_iProver_sP4_1 ) ),
inference(instantiation,[status(thm)],[c_9313]) ).
tcf(c_94719,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1] :
( ( app(nil,cons(X0_iProver_ssItem_1,X0_iProver_sP4_1)) = cons(X0_iProver_ssItem_1,X0_iProver_sP4_1) )
| ~ ssList(cons(X0_iProver_ssItem_1,X0_iProver_sP4_1)) ),
inference(instantiation,[status(thm)],[c_9218]) ).
tcf(c_96723,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1,X2_iProver_sP4_1: iProver_sP4_1,X3_iProver_sP4_1: iProver_sP4_1] :
( ( app(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)),X2_iProver_sP4_1) = app(X1_iProver_sP4_1,X3_iProver_sP4_1) )
| ( X2_iProver_sP4_1 != X3_iProver_sP4_1 )
| ( app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)) != X1_iProver_sP4_1 ) ),
inference(instantiation,[status(thm)],[c_9317]) ).
tcf(c_105024,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1] :
( ( app(app(nil,cons(X0_iProver_ssItem_1,nil)),X0_iProver_sP4_1) = app(cons(X0_iProver_ssItem_1,nil),X1_iProver_sP4_1) )
| ( X0_iProver_sP4_1 != X1_iProver_sP4_1 )
| ( app(nil,cons(X0_iProver_ssItem_1,nil)) != cons(X0_iProver_ssItem_1,nil) ) ),
inference(instantiation,[status(thm)],[c_96723]) ).
tcf(c_127835,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( app(nil,cons(sK50(sK55),X0_iProver_sP4_1)) = cons(sK50(sK55),X0_iProver_sP4_1) )
| ~ ssList(cons(sK50(sK55),X0_iProver_sP4_1)) ),
inference(instantiation,[status(thm)],[c_94719]) ).
tcf(c_127837,plain,
( ( app(nil,cons(sK50(sK55),nil)) = cons(sK50(sK55),nil) )
| ~ ssList(cons(sK50(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_127835]) ).
tcf(c_147761,plain,
( ssList(cons(sK50(sK55),nil))
| ~ ssList(nil)
| ~ ssItem(sK50(sK55)) ),
inference(instantiation,[status(thm)],[c_9233]) ).
tcf(c_163866,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( sK55 = X0_iProver_sP4_1 )
| ( sK55 != cons(sK50(sK55),sK49(sK55)) )
| ( X0_iProver_sP4_1 != cons(sK50(sK55),sK49(sK55)) ) ),
inference(instantiation,[status(thm)],[c_94253]) ).
tcf(c_167719,plain,
( ( sK55 = app(cons(sK50(sK55),nil),sK49(sK55)) )
| ( sK55 != cons(sK50(sK55),sK49(sK55)) )
| ( app(cons(sK50(sK55),nil),sK49(sK55)) != cons(sK50(sK55),sK49(sK55)) ) ),
inference(instantiation,[status(thm)],[c_163866]) ).
tcf(c_167720,plain,
( ( app(cons(sK50(sK55),nil),sK49(sK55)) = cons(sK50(sK55),sK49(sK55)) )
| ~ ssList(sK49(sK55))
| ~ ssItem(sK50(sK55)) ),
inference(instantiation,[status(thm)],[c_9157]) ).
tcf(c_191167,plain,
! [X0_iProver_sP4_1: iProver_sP4_1,X0_iProver_ssItem_1: iProver_ssItem_1,X1_iProver_sP4_1: iProver_sP4_1] :
( ( app(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)),X1_iProver_sP4_1) = sK55 )
| ( sK55 != app(cons(sK50(sK55),nil),sK49(sK55)) )
| ( app(app(X0_iProver_sP4_1,cons(X0_iProver_ssItem_1,nil)),X1_iProver_sP4_1) != app(cons(sK50(sK55),nil),sK49(sK55)) ) ),
inference(instantiation,[status(thm)],[c_94076]) ).
tcf(c_192295,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( app(app(nil,cons(sK50(sK55),nil)),X0_iProver_sP4_1) = sK55 )
| ( sK55 != app(cons(sK50(sK55),nil),sK49(sK55)) )
| ( app(app(nil,cons(sK50(sK55),nil)),X0_iProver_sP4_1) != app(cons(sK50(sK55),nil),sK49(sK55)) ) ),
inference(instantiation,[status(thm)],[c_191167]) ).
tcf(c_192296,plain,
! [X0_iProver_sP4_1: iProver_sP4_1] :
( ( app(app(nil,cons(sK50(sK55),nil)),X0_iProver_sP4_1) = app(cons(sK50(sK55),nil),sK49(sK55)) )
| ( X0_iProver_sP4_1 != sK49(sK55) )
| ( app(nil,cons(sK50(sK55),nil)) != cons(sK50(sK55),nil) ) ),
inference(instantiation,[status(thm)],[c_105024]) ).
tcf(c_199863,plain,
( ( app(app(nil,cons(sK50(sK55),nil)),app(sK49(sK55),nil)) = app(cons(sK50(sK55),nil),sK49(sK55)) )
| ( app(sK49(sK55),nil) != sK49(sK55) )
| ( app(nil,cons(sK50(sK55),nil)) != cons(sK50(sK55),nil) ) ),
inference(instantiation,[status(thm)],[c_192296]) ).
tcf(c_242294,plain,
( ( app(app(nil,cons(sK50(sK55),nil)),app(sK49(sK55),nil)) = sK55 )
| ( sK55 != app(cons(sK50(sK55),nil),sK49(sK55)) )
| ( app(app(nil,cons(sK50(sK55),nil)),app(sK49(sK55),nil)) != app(cons(sK50(sK55),nil),sK49(sK55)) ) ),
inference(instantiation,[status(thm)],[c_192295]) ).
tcf(c_282532,plain,
( ssList(app(sK49(sK55),nil))
| ~ ssList(nil)
| ~ ssList(sK49(sK55)) ),
inference(instantiation,[status(thm)],[c_9220]) ).
tcf(c_296928,plain,
( memberP(nil,sK57(sK50(sK55),nil,app(sK49(sK55),nil)))
| ~ ssList(nil)
| ~ ssItem(sK50(sK55))
| ~ ssList(app(sK49(sK55),nil))
| ( app(app(nil,cons(sK50(sK55),nil)),app(sK49(sK55),nil)) != sK55 ) ),
inference(instantiation,[status(thm)],[c_9138]) ).
tcf(c_296932,plain,
( ssItem(sK57(sK50(sK55),nil,app(sK49(sK55),nil)))
| ~ ssList(nil)
| ~ ssItem(sK50(sK55))
| ~ ssList(app(sK49(sK55),nil))
| ( app(app(nil,cons(sK50(sK55),nil)),app(sK49(sK55),nil)) != sK55 ) ),
inference(instantiation,[status(thm)],[c_9139]) ).
tcf(c_302968,plain,
( ~ ssItem(sK57(sK50(sK55),nil,app(sK49(sK55),nil)))
| ~ memberP(nil,sK57(sK50(sK55),nil,app(sK49(sK55),nil))) ),
inference(instantiation,[status(thm)],[c_9202]) ).
tcf(c_302969,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_302968,c_296928,c_296932,c_282532,c_242294,c_199863,c_167720,c_167719,c_147761,c_127837,c_49801,c_25928,c_16277,c_12784,c_12789,c_12790,c_12379,c_9140,c_9340,c_141,c_262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC248+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 17:12:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.46
% 0.15/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.46
% 0.15/0.46 % Detected problem language: tptp
% 0.15/0.49 % Proving...
% 259.11/38.89 % SZS status Started for theBenchmark.p
% 259.11/38.89 % SZS status Theorem for theBenchmark.p
% 259.11/38.89
% 259.11/38.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 259.11/38.89
% 259.11/38.89 % ------ iProver source info
% 259.11/38.89
% 259.11/38.89 % git: date: 2026-07-19 20:42:38 +0200
% 259.11/38.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 259.11/38.89 % git: non_committed_changes: false
% 259.11/38.89
% 259.11/38.89 % ------ Parsing...
% 259.11/38.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 259.11/38.89
% 259.11/38.89 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 259.11/38.89
% 259.11/38.89 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 259.11/38.89
% 259.11/38.89 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 259.11/38.89 % ------ Proving...
% 259.11/38.89 % ------ Problem Properties
% 259.11/38.89
% 259.11/38.89 %
% 259.11/38.89 % clauses 194
% 259.11/38.89 % conjectures 14
% 259.11/38.89 % EPR 55
% 259.11/38.89 % Horn 126
% 259.11/38.89 % unary 23
% 259.11/38.89 % binary 40
% 259.11/38.89 % lits 664
% 259.11/38.89 % lits eq 89
% 259.11/38.89 % fd_pure 0
% 259.11/38.89 % fd_pseudo 0
% 259.11/38.89 % fd_cond 21
% 259.11/38.89 % fd_pseudo_cond 14
% 259.11/38.89 % AC symbols 0
% 259.11/38.89
% 259.11/38.89 % ------ Input Options Time Limit: Unbounded
% 259.11/38.89
% 259.11/38.89
% 259.11/38.89 % ------
% 259.11/38.89 % Current options:
% 259.11/38.89 % ------
% 259.11/38.89
% 259.11/38.89
% 259.11/38.89 %
% 259.11/38.89
% 259.11/38.89 % ------ Proving...
% 259.11/38.89 %
% 259.11/38.89
% 259.11/38.89 % SZS status Theorem for theBenchmark.p
% 259.11/38.89
% 259.11/38.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 259.11/38.89
% 259.11/38.89
%------------------------------------------------------------------------------