%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC100+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 03:07:53 PM UTC 2026
% Result : Theorem 4.20s 6.33s
% Output : CNFRefutation 4.20s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f546ERROR: Could not build tree for root c_14029ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ( frontsegP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ( frontsegP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f158,plain,
! [X0] :
( ~ ssList(X0)
| ( frontsegP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ( ~ frontsegP(X1,X0)
| ~ neq(X0,nil) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ( ~ frontsegP(X1,X0)
| ~ neq(X0,nil) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f283,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ frontsegP(nil,X0)
| nil = X0 )
& ( nil != X0
| frontsegP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f158]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ( ~ frontsegP(sK54,sK53)
| ~ neq(sK53,nil) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != sK55
| nil = sK56 )
& ssList(sK57)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != sK55
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK57
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(sK55)
& sK56 = app(sK55,sK57)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f429,plain,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f283]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ frontsegP(sK54,sK53)
| ~ neq(sK53,nil)
| nil = sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil != sK55
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
ssList(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK56 = app(sK55,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
( ~ frontsegP(sK56,sK55)
| ~ neq(sK55,nil)
| nil = sK56 ),
inference(definition_unfolding,[],[f502,f510,f509,f510,f509]) ).
fof(f513,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f501,f509,f510]) ).
fof(f516,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f509]) ).
fof(f520,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_139,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f546]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_182,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f429]) ).
tcf(c_246,negated_conjecture,
app(sK55,sK57) = sK56,
inference(cnf_transformation,[],[f508]) ).
tcf(c_249,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f505]) ).
tcf(c_250,negated_conjecture,
( ( nil = sK56 )
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_252,negated_conjecture,
( ( nil = sK56 )
| ~ frontsegP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_253,negated_conjecture,
( neq(sK56,nil)
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f513]) ).
tcf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f516]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
tcf(c_3293,plain,
! [X0: $i,X1: $i] :
( ( nil = sK56 )
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK56,sK55)
| ( X1 != nil )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_252]) ).
tcf(c_3294,plain,
( ( sK55 = nil )
| ( nil = sK56 )
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ frontsegP(sK56,sK55) ),
inference(unflattening,[status(thm)],[c_3293]) ).
tcf(c_3295,plain,
( ( sK55 = nil )
| ( nil = sK56 )
| ~ frontsegP(sK56,sK55) ),
inference(global_subsumption_just,[status(thm)],[c_3294,c_258,c_141,c_3294]) ).
tcf(c_3314,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( nil != sK55 )
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_253]) ).
tcf(c_3315,plain,
( ~ ssList(nil)
| ( nil != sK55 )
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3314]) ).
tcf(c_3316,plain,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_3315,c_141,c_250,c_3315]) ).
tcf(c_8984,definition,
iPr_def_10 = app(sK55,sK57),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8986,plain,
nil != sK55,
inference(demodulation,[status(thm)],[c_3316]) ).
tcf(c_8987,plain,
( ( sK55 = nil )
| ( nil = sK56 )
| ~ frontsegP(sK56,sK55) ),
inference(demodulation,[status(thm)],[c_3295]) ).
tcf(c_8988,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_258]) ).
tcf(c_8990,negated_conjecture,
ssList(sK57),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8993,negated_conjecture,
iPr_def_10 = sK56,
inference(demodulation,[status(thm)],[c_246,c_8984]) ).
tcf(c_11853,plain,
( ( nil = iPr_def_10 )
| ( nil = sK55 )
| ~ frontsegP(iPr_def_10,sK55) ),
inference(light_normalisation,[status(thm)],[c_8987,c_8993]) ).
tcf(c_11854,plain,
( ( nil = iPr_def_10 )
| ~ frontsegP(iPr_def_10,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11853,c_8986]) ).
tcf(c_11933,plain,
( frontsegP(iPr_def_10,sK55)
| ~ ssList(sK57)
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8984,c_380]) ).
tcf(c_11934,plain,
frontsegP(iPr_def_10,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_11933,c_8990,c_8988]) ).
tcf(c_11935,plain,
nil = iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_11854,c_11934]) ).
tcf(c_11949,plain,
sK55 != iPr_def_10,
inference(demodulation,[status(thm)],[c_8986,c_11935]) ).
tcf(c_14015,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ ssList(X0)
| ~ frontsegP(iPr_def_10,X0) ),
inference(light_normalisation,[status(thm)],[c_182,c_11935]) ).
tcf(c_14026,plain,
( ( sK55 = iPr_def_10 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_11934,c_14015]) ).
tcf(c_14029,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14026,c_11949,c_8988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC100+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.39 % Computer : n016.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Thu Sep 24 16:28:05 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/5.43 Running first-order theorem proving
% 0.17/5.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.45
% 0.17/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.45
% 0.17/5.45 % Detected problem language: tptp
% 0.17/5.46 % Proving...
% 4.20/6.33 % SZS status Started for theBenchmark.p
% 4.20/6.33 % SZS status Theorem for theBenchmark.p
% 4.20/6.33
% 4.20/6.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.20/6.33
% 4.20/6.33 % ------ iProver source info
% 4.20/6.33
% 4.20/6.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.20/6.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.20/6.33 % git: non_committed_changes: false
% 4.20/6.33
% 4.20/6.33 % ------ Parsing...
% 4.20/6.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.20/6.33
% 4.20/6.33 % ------ 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 %
% 4.20/6.33
% 4.20/6.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.20/6.33
% 4.20/6.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.20/6.33 % ------ Proving...
% 4.20/6.33 % ------ Problem Properties
% 4.20/6.33
% 4.20/6.33 %
% 4.20/6.33 % clauses 190
% 4.20/6.33 % conjectures 6
% 4.20/6.33 % EPR 57
% 4.20/6.33 % Horn 121
% 4.20/6.33 % unary 23
% 4.20/6.33 % binary 40
% 4.20/6.33 % lits 638
% 4.20/6.33 % lits eq 87
% 4.20/6.33 % fd_pure 0
% 4.20/6.33 % fd_pseudo 0
% 4.20/6.33 % fd_cond 21
% 4.20/6.33 % fd_pseudo_cond 14
% 4.20/6.33 % AC symbols 0
% 4.20/6.33
% 4.20/6.33 % ------ Schedule dynamic 5 is on
% 4.20/6.33
% 4.20/6.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.20/6.33
% 4.20/6.33
% 4.20/6.33 % ------
% 4.20/6.33 % Current options:
% 4.20/6.33 % ------
% 4.20/6.33
% 4.20/6.33
% 4.20/6.33 %
% 4.20/6.33
% 4.20/6.33 % ------ Proving...
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% 4.20/6.33 % SZS status Theorem for theBenchmark.p
% 4.20/6.33
% 4.20/6.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.20/6.33
% 4.20/6.33
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