%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC377-1 : 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 : n003.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 03:09:32 PM UTC 2026
% Result : Unsatisfiable 6.53s 2.70s
% Output : CNFRefutation 6.53s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f229ERROR: Could not build tree for root c_30946ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
fof(f99,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| nil != cons(X0,X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f101,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f101]) ).
fof(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f150,axiom,
! [X2,X0,X1] :
( memberP(cons(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause139) ).
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause140) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause141) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
fof(f162,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause150) ).
fof(f170,axiom,
! [X2,X0,X1] :
( memberP(X0,X2)
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ memberP(app(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause158) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( memberP(sk1,sk5)
| memberP(sk2,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f212,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk6,nil),sk7) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f213,plain,
( ~ neq(sk4,nil)
| sk3 = app(cons(sk6,nil),sk7) ),
inference(reorient_equations,[],[f212]) ).
fof(f214,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk7,cons(sk6,nil)) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f215,plain,
( ~ neq(sk4,nil)
| sk4 = app(sk7,cons(sk6,nil)) ),
inference(reorient_equations,[],[f214]) ).
fof(f218,plain,
( memberP(sk3,sk5)
| memberP(sk4,sk5) ),
inference(definition_unfolding,[],[f207,f204,f205]) ).
fof(f219,plain,
( ~ memberP(sk3,sk5)
| ~ memberP(sk4,sk5) ),
inference(definition_unfolding,[],[f208,f204,f205]) ).
tcf(c_250,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_251,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_252,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_253,negated_conjecture,
( memberP(sk4,sk5)
| memberP(sk3,sk5) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_254,negated_conjecture,
( ~ memberP(sk4,sk5)
| ~ memberP(sk3,sk5) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_255,negated_conjecture,
( ( sk3 = nil )
| ( sk4 != nil ) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_256,negated_conjecture,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_257,negated_conjecture,
( ssList(sk7)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_258,negated_conjecture,
( ( app(cons(sk6,nil),sk7) = sk3 )
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_259,negated_conjecture,
( ( app(sk7,cons(sk6,nil)) = sk4 )
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| memberP(X0,X2)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(cons(X2,X0),X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_267,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_274,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_275,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_277,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X0,X2) ) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(X0,X2),X1) = app(X0,app(X2,X1)) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_289,plain,
( ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(instantiation,[status(thm)],[c_277]) ).
tcf(c_297,plain,
( neq(nil,nil)
| ( nil = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_279]) ).
tcf(c_316,plain,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
inference(prop_impl_just,[status(thm)],[c_256]) ).
tcf(c_318,plain,
( ssList(sk7)
| ~ neq(sk4,nil) ),
inference(prop_impl_just,[status(thm)],[c_257]) ).
tcf(c_320,plain,
( ( app(cons(sk6,nil),sk7) = sk3 )
| ~ neq(sk4,nil) ),
inference(prop_impl_just,[status(thm)],[c_258]) ).
tcf(c_322,plain,
( ( app(sk7,cons(sk6,nil)) = sk4 )
| ~ neq(sk4,nil) ),
inference(prop_impl_just,[status(thm)],[c_259]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(sk7,cons(sk6,nil)) = sk4 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_322,c_279]) ).
tcf(c_924,plain,
( ( sk4 = nil )
| ( app(sk7,cons(sk6,nil)) = sk4 )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_923]) ).
tcf(c_925,plain,
( ( sk4 = nil )
| ( app(sk7,cons(sk6,nil)) = sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_924,c_251,c_275,c_924]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(cons(sk6,nil),sk7) = sk3 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_279]) ).
tcf(c_948,plain,
( ( sk4 = nil )
| ( app(cons(sk6,nil),sk7) = sk3 )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_947]) ).
tcf(c_949,plain,
( ( sk4 = nil )
| ( app(cons(sk6,nil),sk7) = sk3 ) ),
inference(global_subsumption_just,[status(thm)],[c_948,c_251,c_275,c_948]) ).
tcf(c_971,plain,
! [X0: $i,X1: $i] :
( ssList(sk7)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_318,c_279]) ).
tcf(c_972,plain,
( ssList(sk7)
| ( sk4 = nil )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_971]) ).
tcf(c_973,plain,
( ssList(sk7)
| ( sk4 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_972,c_251,c_275,c_972]) ).
tcf(c_995,plain,
! [X0: $i,X1: $i] :
( ssItem(sk6)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_316,c_279]) ).
tcf(c_996,plain,
( ssItem(sk6)
| ( sk4 = nil )
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(unflattening,[status(thm)],[c_995]) ).
tcf(c_997,plain,
( ssItem(sk6)
| ( sk4 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_996,c_251,c_275,c_996]) ).
tcf(c_1027,plain,
( ssItem(sk6)
| ( sk4 = nil ) ),
inference(prop_impl_just,[status(thm)],[c_251,c_275,c_996]) ).
tcf(c_1029,plain,
( ssList(sk7)
| ( sk4 = nil ) ),
inference(prop_impl_just,[status(thm)],[c_251,c_275,c_972]) ).
tcf(c_1031,plain,
( ( app(cons(sk6,nil),sk7) = sk3 )
| ( sk4 = nil ) ),
inference(prop_impl_just,[status(thm)],[c_949]) ).
tcf(c_1032,plain,
( ( sk4 = nil )
| ( app(cons(sk6,nil),sk7) = sk3 ) ),
inference(renaming,[status(thm)],[c_1031]) ).
tcf(c_1033,plain,
( ( app(sk7,cons(sk6,nil)) = sk4 )
| ( sk4 = nil ) ),
inference(prop_impl_just,[status(thm)],[c_925]) ).
tcf(c_1034,plain,
( ( sk4 = nil )
| ( app(sk7,cons(sk6,nil)) = sk4 ) ),
inference(renaming,[status(thm)],[c_1033]) ).
tcf(c_1560,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(X0,X2) = cons(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2361,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,X0),nil) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_284,c_274]) ).
tcf(c_2428,plain,
! [X0: $i] :
( ( app(cons(X0,nil),nil) = cons(X0,nil) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_275,c_2361]) ).
tcf(c_2466,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk3) = cons(X0,sk3) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_250,c_269]) ).
tcf(c_2468,plain,
! [X0: $i] :
( ( sk4 = nil )
| ( app(cons(X0,nil),sk7) = cons(X0,sk7) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_1029,c_269]) ).
tcf(c_2562,plain,
app(cons(sk5,nil),sk3) = cons(sk5,sk3),
inference(superposition,[status(thm)],[c_252,c_2466]) ).
tcf(c_2618,plain,
( ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(instantiation,[status(thm)],[c_267]) ).
tcf(c_2627,plain,
! [X0: $i] :
( ssList(cons(sk5,X0))
| ~ ssItem(sk5)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_284]) ).
tcf(c_2628,plain,
( ssList(cons(sk5,nil))
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_2627]) ).
tcf(c_2661,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ( sk4 = nil )
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0) ),
inference(superposition,[status(thm)],[c_1034,c_263]) ).
tcf(c_2713,plain,
! [X0: $i] :
( memberP(sk3,X0)
| ( sk4 = nil )
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0) ),
inference(superposition,[status(thm)],[c_1032,c_264]) ).
tcf(c_2714,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ( sk4 = nil )
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(sk7,X0)
| ~ ssList(cons(sk6,nil)) ),
inference(superposition,[status(thm)],[c_1034,c_264]) ).
tcf(c_2782,plain,
! [X0: $i] :
( memberP(sk7,X0)
| memberP(cons(sk6,nil),X0)
| ( sk4 = nil )
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(sk3,X0)
| ~ ssList(cons(sk6,nil)) ),
inference(superposition,[status(thm)],[c_1032,c_262]) ).
tcf(c_2783,plain,
! [X0: $i] :
( memberP(sk7,X0)
| memberP(cons(sk6,nil),X0)
| ( sk4 = nil )
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ~ ssList(cons(sk6,nil)) ),
inference(superposition,[status(thm)],[c_1034,c_262]) ).
tcf(c_2826,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk3,sk5)
| ( X1 != sk5 )
| ( X0 != sk3 ) ),
inference(instantiation,[status(thm)],[c_1565]) ).
tcf(c_2846,plain,
app(cons(sk5,nil),nil) = cons(sk5,nil),
inference(superposition,[status(thm)],[c_252,c_2428]) ).
tcf(c_2979,plain,
! [X0: $i,X1: $i] :
( ( app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_250,c_287]) ).
tcf(c_2980,plain,
! [X0: $i,X1: $i] :
( ( app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_251,c_287]) ).
tcf(c_3288,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk3 )
| ( sk3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1562]) ).
tcf(c_3289,plain,
( ( nil = sk3 )
| ( nil != nil )
| ( sk3 != nil ) ),
inference(instantiation,[status(thm)],[c_3288]) ).
tcf(c_3657,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(cons(sk5,nil))
| ( app(cons(sk5,nil),X0) != cons(sk5,sk3) ) ),
inference(superposition,[status(thm)],[c_2562,c_286]) ).
tcf(c_3716,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(X0)
| ~ ssList(cons(sk5,nil))
| ( app(cons(sk5,nil),X0) != cons(sk5,sk3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3657,c_250]) ).
tcf(c_3846,plain,
! [X0: $i] :
( memberP(X0,sk5)
| ~ memberP(sk3,sk5)
| ( sk5 != sk5 )
| ( X0 != sk3 ) ),
inference(instantiation,[status(thm)],[c_2826]) ).
tcf(c_3847,plain,
sk5 = sk5,
inference(instantiation,[status(thm)],[c_1560]) ).
tcf(c_3848,plain,
( memberP(nil,sk5)
| ~ memberP(sk3,sk5)
| ( nil != sk3 )
| ( sk5 != sk5 ) ),
inference(instantiation,[status(thm)],[c_3846]) ).
tcf(c_3897,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cons(sk5,X0) = cons(X2,X1) )
| ( sk5 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1566]) ).
tcf(c_5697,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk4,sk5)
| ( X1 != sk5 )
| ( X0 != sk4 ) ),
inference(instantiation,[status(thm)],[c_1565]) ).
tcf(c_5803,plain,
! [X0: $i] :
( ( app(app(sk3,X0),sk4) = app(sk3,app(X0,sk4)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_251,c_2979]) ).
tcf(c_5920,plain,
! [X0: $i] :
( ssList(app(X0,sk3))
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_288]) ).
tcf(c_5948,plain,
! [X0: $i] :
( ssList(app(sk3,X0))
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_288]) ).
tcf(c_6652,plain,
app(app(sk3,sk4),sk4) = app(sk3,app(sk4,sk4)),
inference(superposition,[status(thm)],[c_251,c_5803]) ).
tcf(c_7141,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(sk3,sk4),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ ssList(app(sk3,sk4))
| ~ memberP(app(sk3,app(sk4,sk4)),X0) ),
inference(superposition,[status(thm)],[c_6652,c_262]) ).
tcf(c_7173,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(sk3,sk4),X0)
| ~ ssItem(X0)
| ~ ssList(app(sk3,sk4))
| ~ memberP(app(sk3,app(sk4,sk4)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7141,c_251]) ).
tcf(c_7211,plain,
! [X0: $i,X1: $i] :
( ( cons(sk5,X0) = cons(sk5,X1) )
| ( sk5 != sk5 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3897]) ).
tcf(c_7408,plain,
! [X0: $i] :
( ( app(app(sk4,X0),sk3) = app(sk4,app(X0,sk3)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_250,c_2980]) ).
tcf(c_7560,plain,
app(app(sk4,sk3),sk3) = app(sk4,app(sk3,sk3)),
inference(superposition,[status(thm)],[c_250,c_7408]) ).
tcf(c_7663,plain,
! [X0: $i] :
( memberP(sk3,X0)
| memberP(app(sk4,sk3),X0)
| ~ ssList(sk3)
| ~ ssItem(X0)
| ~ ssList(app(sk4,sk3))
| ~ memberP(app(sk4,app(sk3,sk3)),X0) ),
inference(superposition,[status(thm)],[c_7560,c_262]) ).
tcf(c_7695,plain,
! [X0: $i] :
( memberP(sk3,X0)
| memberP(app(sk4,sk3),X0)
| ~ ssItem(X0)
| ~ ssList(app(sk4,sk3))
| ~ memberP(app(sk4,app(sk3,sk3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7663,c_250]) ).
tcf(c_9539,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk4 )
| ( sk4 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1562]) ).
tcf(c_9540,plain,
( ( nil = sk4 )
| ( nil != nil )
| ( sk4 != nil ) ),
inference(instantiation,[status(thm)],[c_9539]) ).
tcf(c_11209,plain,
! [X0: $i] :
( ( cons(sk5,sk3) = cons(sk5,X0) )
| ( sk5 != sk5 )
| ( sk3 != X0 ) ),
inference(instantiation,[status(thm)],[c_7211]) ).
tcf(c_11211,plain,
( ( cons(sk5,sk3) = cons(sk5,nil) )
| ( sk5 != sk5 )
| ( sk3 != nil ) ),
inference(instantiation,[status(thm)],[c_11209]) ).
tcf(c_16616,plain,
( ( sk4 = nil )
| ( app(cons(sk6,nil),sk7) = cons(sk6,sk7) ) ),
inference(superposition,[status(thm)],[c_1027,c_2468]) ).
tcf(c_16754,plain,
( ( sk4 = nil )
| ( cons(sk6,sk7) = sk3 ) ),
inference(superposition,[status(thm)],[c_1032,c_16616]) ).
tcf(c_16840,plain,
( ( sk4 = nil )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( sk3 != nil ) ),
inference(superposition,[status(thm)],[c_16754,c_272]) ).
tcf(c_16844,plain,
! [X0: $i] :
( memberP(sk3,X0)
| ( sk4 = nil )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(superposition,[status(thm)],[c_16754,c_265]) ).
tcf(c_17303,plain,
( ( sk4 = nil )
| ( sk3 != nil ) ),
inference(global_subsumption_just,[status(thm)],[c_16840,c_251,c_275,c_972,c_996,c_16840]) ).
tcf(c_23546,plain,
! [X0: $i] :
( memberP(X0,sk5)
| ~ memberP(sk4,sk5)
| ( sk5 != sk5 )
| ( X0 != sk4 ) ),
inference(instantiation,[status(thm)],[c_5697]) ).
tcf(c_23547,plain,
( memberP(nil,sk5)
| ~ memberP(sk4,sk5)
| ( nil != sk4 )
| ( sk5 != sk5 ) ),
inference(instantiation,[status(thm)],[c_23546]) ).
tcf(c_24583,plain,
( ssList(app(sk4,sk3))
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_5920]) ).
tcf(c_24588,plain,
( ssList(app(sk3,sk4))
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_5948]) ).
tcf(c_24821,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(X0)
| ( app(cons(sk5,nil),X0) != cons(sk5,sk3) ) ),
inference(global_subsumption_just,[status(thm)],[c_3716,c_252,c_275,c_2628,c_3716]) ).
tcf(c_24832,plain,
( ( sk3 = nil )
| ~ ssList(nil)
| ( cons(sk5,sk3) != cons(sk5,nil) ) ),
inference(superposition,[status(thm)],[c_2846,c_24821]) ).
tcf(c_24836,plain,
( ( sk3 = nil )
| ( cons(sk5,sk3) != cons(sk5,nil) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24832,c_275]) ).
tcf(c_25992,plain,
cons(sk5,sk3) != cons(sk5,nil),
inference(global_subsumption_just,[status(thm)],[c_24836,c_252,c_275,c_253,c_289,c_297,c_2618,c_3289,c_3848,c_3847,c_9540,c_17303,c_23547,c_24836]) ).
tcf(c_30521,plain,
! [X0: $i] :
( ssList(cons(sk6,X0))
| ~ ssItem(sk6)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_284]) ).
tcf(c_30522,plain,
( ssList(cons(sk6,nil))
| ~ ssItem(sk6)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_30521]) ).
tcf(c_30849,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(sk3,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(app(sk3,app(sk4,sk4)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_7173,c_251,c_250,c_7173,c_24588]) ).
tcf(c_30860,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(sk3,sk4),X0)
| ~ ssList(sk3)
| ~ ssItem(X0)
| ~ memberP(sk3,X0)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_264,c_30849]) ).
tcf(c_30864,plain,
! [X0: $i] :
( memberP(sk4,X0)
| memberP(app(sk3,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0)
| ~ ssList(app(sk4,sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30860,c_250]) ).
tcf(c_30878,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_30864,c_275,c_255,c_973,c_997,c_2661,c_2714,c_2782,c_3847,c_11211,c_25992,c_30522]) ).
tcf(c_30879,plain,
! [X0: $i] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(renaming,[status(thm)],[c_30878]) ).
tcf(c_30887,plain,
( memberP(sk4,sk5)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_253,c_30879]) ).
tcf(c_30889,plain,
memberP(sk4,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_30887,c_252]) ).
tcf(c_30893,plain,
~ memberP(sk3,sk5),
inference(backward_subsumption_resolution,[status(thm)],[c_254,c_30889]) ).
tcf(c_30907,plain,
! [X0: $i] :
( memberP(sk3,X0)
| memberP(app(sk4,sk3),X0)
| ~ ssItem(X0)
| ~ memberP(app(sk4,app(sk3,sk3)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_7695,c_251,c_250,c_7695,c_24583]) ).
tcf(c_30918,plain,
! [X0: $i] :
( memberP(sk3,X0)
| memberP(app(sk4,sk3),X0)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ~ ssList(app(sk3,sk3)) ),
inference(superposition,[status(thm)],[c_264,c_30907]) ).
tcf(c_30922,plain,
! [X0: $i] :
( memberP(sk3,X0)
| memberP(app(sk4,sk3),X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ~ ssList(app(sk3,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30918,c_251]) ).
tcf(c_30936,plain,
! [X0: $i] :
( memberP(sk3,X0)
| ~ memberP(sk4,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_30922,c_252,c_251,c_275,c_253,c_289,c_255,c_297,c_972,c_996,c_2618,c_2713,c_2783,c_3289,c_3848,c_3847,c_9540,c_16844,c_17303,c_23547,c_30522]) ).
tcf(c_30937,plain,
! [X0: $i] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
inference(renaming,[status(thm)],[c_30936]) ).
tcf(c_30945,plain,
( memberP(sk3,sk5)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_30889,c_30937]) ).
tcf(c_30946,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_30945,c_30893,c_252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC377-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 17:57:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 6.53/2.70 % SZS status Started for theBenchmark.p
% 6.53/2.70 % SZS status Unsatisfiable for theBenchmark.p
% 6.53/2.70
% 6.53/2.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.53/2.70
% 6.53/2.70 % ------ iProver source info
% 6.53/2.70
% 6.53/2.70 % git: date: 2026-07-19 20:42:38 +0200
% 6.53/2.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.53/2.70 % git: non_committed_changes: false
% 6.53/2.70
% 6.53/2.70 % ------ Parsing...% successful
% 6.53/2.70
% 6.53/2.70
% 6.53/2.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.53/2.70
% 6.53/2.70 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 6.53/2.70
% 6.53/2.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.53/2.70
% 6.53/2.70 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.53/2.70 % ------ Proving...
% 6.53/2.70 % ------ Problem Properties
% 6.53/2.70
% 6.53/2.70 %
% 6.53/2.70 % clauses 35
% 6.53/2.70 % conjectures 6
% 6.53/2.70 % EPR 10
% 6.53/2.70 % Horn 28
% 6.53/2.70 % unary 5
% 6.53/2.70 % binary 10
% 6.53/2.70 % lits 113
% 6.53/2.70 % lits eq 29
% 6.53/2.70 % fd_pure 0
% 6.53/2.70 % fd_pseudo 0
% 6.53/2.70 % fd_cond 2
% 6.53/2.70 % fd_pseudo_cond 5
% 6.53/2.70 % AC symbols 0
% 6.53/2.70
% 6.53/2.70 % ------ Schedule dynamic 5 is on
% 6.53/2.70
% 6.53/2.70 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.53/2.70
% 6.53/2.70
% 6.53/2.70 % ------
% 6.53/2.70 % Current options:
% 6.53/2.70 % ------
% 6.53/2.70
% 6.53/2.70
% 6.53/2.70 %
% 6.53/2.70
% 6.53/2.70 % ------ Proving...
% 6.53/2.70 %
% 6.53/2.70
% 6.53/2.70 % SZS status Unsatisfiable for theBenchmark.p
% 6.53/2.70
% 6.53/2.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.53/2.71
%------------------------------------------------------------------------------