%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC323+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 : n016.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 03:09:18 PM UTC 2026
% Result : Theorem 1.84s 11.49s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f543ERROR: Could not build tree for root c_12413ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(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] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X2
| app(cons(X6,nil),X7) != X3 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,X4) = X0
& app(X4,X5) = X1
& ssList(X5) )
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X2
| app(cons(X6,nil),X7) != X3 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,X4) = X0
& app(X4,X5) = X1
& ssList(X5) )
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
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] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X2
& app(cons(X6,nil),X7) = X3 ) ) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(X5,X4) != X0
| app(X4,X5) != X1
| ~ ssList(X5) )
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X2
& app(cons(X6,nil),X7) = X3 ) ) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(X5,X4) != X0
| app(X4,X5) != X1
| ~ ssList(X5) )
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ neq(sK56,nil)
| ( ssItem(sK57)
& ssList(sK58)
& sK55 = app(sK58,cons(sK57,nil))
& sK56 = app(cons(sK57,nil),sK58) ) )
& ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( app(X5,X4) != sK53
| app(X4,X5) != sK54
| ~ ssList(X5) )
| ~ ssList(X4) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X6,sK57),skolemize(X7,sK58)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| sK55 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( ~ neq(sK56,nil)
| sK56 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
! [X4,X5] :
( app(X5,X4) != sK53
| app(X4,X5) != sK54
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
! [X4,X5] :
( app(X5,X4) != sK55
| app(X4,X5) != sK56
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f505,f507,f506]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_229,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f543]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(X1,X0) != sK56 )
| ( app(X0,X1) != sK55 ) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_247,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_248,negated_conjecture,
( ( app(cons(sK57,nil),sK58) = sK56 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_249,negated_conjecture,
( ( app(sK58,cons(sK57,nil)) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_250,negated_conjecture,
( ssList(sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_251,negated_conjecture,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_254,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_296,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_369,plain,
app(nil,nil) = nil,
inference(global_subsumption_just,[status(thm)],[c_229,c_141,c_296]) ).
tcf(c_3252,plain,
! [X0: $i,X1: $i] :
( ssItem(sK57)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_251]) ).
tcf(c_3253,plain,
( ssItem(sK57)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3252]) ).
tcf(c_3254,plain,
( ssItem(sK57)
| ( sK56 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3253,c_254,c_141,c_3253]) ).
tcf(c_3262,plain,
! [X0: $i,X1: $i] :
( ssList(sK58)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_250]) ).
tcf(c_3263,plain,
( ssList(sK58)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3262]) ).
tcf(c_3264,plain,
( ssList(sK58)
| ( sK56 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3263,c_254,c_141,c_3263]) ).
tcf(c_3272,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(sK58,cons(sK57,nil)) = sK55 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_249]) ).
tcf(c_3273,plain,
( ( sK56 = nil )
| ( app(sK58,cons(sK57,nil)) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3272]) ).
tcf(c_3274,plain,
( ( sK56 = nil )
| ( app(sK58,cons(sK57,nil)) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_3273,c_254,c_141,c_3273]) ).
tcf(c_3282,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(cons(sK57,nil),sK58) = sK56 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_248]) ).
tcf(c_3283,plain,
( ( sK56 = nil )
| ( app(cons(sK57,nil),sK58) = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3282]) ).
tcf(c_3284,plain,
( ( sK56 = nil )
| ( app(cons(sK57,nil),sK58) = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_3283,c_254,c_141,c_3283]) ).
tcf(c_8939,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8940,definition,
iPr_def_11 = app(iPr_def_10,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8941,definition,
iPr_def_12 = app(sK58,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8942,plain,
( ( iPr_def_11 = sK56 )
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3284,c_8939,c_8940]) ).
tcf(c_8943,plain,
( ( iPr_def_12 = sK55 )
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3274,c_8941]) ).
tcf(c_8944,plain,
( ssList(sK58)
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3264]) ).
tcf(c_8945,plain,
( ssItem(sK57)
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3254]) ).
tcf(c_8949,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(X1,X0) != sK56 )
| ( app(X0,X1) != sK55 ) ),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_11828,plain,
( ~ ssList(nil)
| ( nil != sK55 )
| ( app(nil,nil) != sK56 ) ),
inference(superposition,[status(thm)],[c_369,c_8949]) ).
tcf(c_11829,plain,
( ~ ssList(nil)
| ( nil != sK55 )
| ( nil != sK56 ) ),
inference(light_normalisation,[status(thm)],[c_11828,c_369]) ).
tcf(c_11872,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_11829,c_141,c_247,c_11829]) ).
tcf(c_11875,plain,
sK56 = iPr_def_11,
inference(superposition,[status(thm)],[c_8942,c_11872]) ).
tcf(c_11878,plain,
nil != iPr_def_11,
inference(demodulation,[status(thm)],[c_11872,c_11875]) ).
tcf(c_11879,plain,
( ( sK55 = iPr_def_12 )
| ( nil = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_8943,c_11875]) ).
tcf(c_11881,plain,
( ssItem(sK57)
| ( nil = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_8945,c_11875]) ).
tcf(c_11882,plain,
( ssList(sK58)
| ( nil = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_8944,c_11875]) ).
tcf(c_11883,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(X1,X0) != iPr_def_11 )
| ( app(X0,X1) != sK55 ) ),
inference(demodulation,[status(thm)],[c_8949,c_11875]) ).
tcf(c_11895,plain,
ssList(sK58),
inference(backward_subsumption_resolution,[status(thm)],[c_11882,c_11878]) ).
tcf(c_11896,plain,
ssItem(sK57),
inference(backward_subsumption_resolution,[status(thm)],[c_11881,c_11878]) ).
tcf(c_11897,plain,
sK55 = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_11879,c_11878]) ).
tcf(c_11901,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(X1,X0) != iPr_def_11 )
| ( app(X0,X1) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_11883,c_11897]) ).
tcf(c_11923,plain,
( ~ ssList(iPr_def_10)
| ~ ssList(sK58)
| ( app(sK58,iPr_def_10) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8940,c_11901]) ).
tcf(c_11924,plain,
( ~ ssList(iPr_def_10)
| ~ ssList(sK58) ),
inference(ground_joinability,[status(thm)],[c_11923,c_8941]) ).
tcf(c_11925,plain,
~ ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_11924,c_11895]) ).
tcf(c_12410,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8939,c_140]) ).
tcf(c_12413,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12410,c_11925,c_141,c_11896]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC323+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.57 % Computer : n016.cluster.edu
% 0.11/10.57 % Model : x86_64 x86_64
% 0.11/10.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.57 % Memory : 8046.5625MB
% 0.11/10.57 % OS : Linux 6.8.0-71-generic
% 0.11/10.57 % CPULimit : 300
% 0.11/10.57 % WCLimit : 300
% 0.11/10.57 % DateTime : Thu Sep 24 17:42:39 UTC 2026
% 0.11/10.58 % CPUTime :
% 0.11/10.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.61 Running first-order theorem proving
% 0.15/10.61 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
% 0.15/10.62
% 0.15/10.62 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.62
% 0.15/10.63 % Detected problem language: tptp
% 0.15/10.64 % Proving...
% 1.84/11.49 % SZS status Started for theBenchmark.p
% 1.84/11.49 % SZS status Theorem for theBenchmark.p
% 1.84/11.49
% 1.84/11.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/11.49
% 1.84/11.49 % ------ iProver source info
% 1.84/11.49
% 1.84/11.49 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/11.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/11.49 % git: non_committed_changes: false
% 1.84/11.49
% 1.84/11.49 % ------ Parsing...
% 1.84/11.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/11.49
% 1.84/11.49 % ------ 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: 5 0s sf_e pe_s pe_e %
% 1.84/11.49
% 1.84/11.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/11.49
% 1.84/11.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/11.49 % ------ Proving...
% 1.84/11.49 % ------ Problem Properties
% 1.84/11.49
% 1.84/11.49 %
% 1.84/11.49 % clauses 191
% 1.84/11.49 % conjectures 4
% 1.84/11.49 % EPR 56
% 1.84/11.49 % Horn 119
% 1.84/11.49 % unary 21
% 1.84/11.49 % binary 45
% 1.84/11.49 % lits 637
% 1.84/11.49 % lits eq 91
% 1.84/11.49 % fd_pure 0
% 1.84/11.49 % fd_pseudo 0
% 1.84/11.49 % fd_cond 21
% 1.84/11.49 % fd_pseudo_cond 14
% 1.84/11.49 % AC symbols 0
% 1.84/11.49
% 1.84/11.49 % ------ Schedule dynamic 5 is on
% 1.84/11.49
% 1.84/11.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.84/11.49
% 1.84/11.49
% 1.84/11.49 % ------
% 1.84/11.49 % Current options:
% 1.84/11.49 % ------
% 1.84/11.49
% 1.84/11.49
% 1.84/11.49 %
% 1.84/11.49
% 1.84/11.49 % ------ Proving...
% 1.84/11.49 %
% 1.84/11.49
% 1.84/11.49 % SZS status Theorem for theBenchmark.p
% 1.84/11.49
% 1.84/11.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/11.49
% 1.84/11.49
%------------------------------------------------------------------------------