%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC013+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 : n026.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 03:07:30 PM UTC 2026
% Result : Theorem 3.70s 1.28s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f557ERROR: Could not build tree for root c_12310ERROR: 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(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X1)
& hd(X1) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X0 = X6
& ssList(X6) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& hd(X3) = X5
& cons(X5,nil) = X4
& ssItem(X5) )
& X2 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| 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)
| ~ neq(X1,nil) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X1)
& hd(X1) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X0 = X6
& ssList(X6) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& hd(X3) = X5
& cons(X5,nil) = X4
& ssItem(X5) )
& X2 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| 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(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f126]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X6] :
( ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| X0 != X6
| ~ ssList(X6) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& neq(X1,nil) ) )
& 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)
& neq(X1,nil) )
| ( ! [X6] :
( ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| X0 != X6
| ~ ssList(X6) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& neq(X1,nil) ) )
& 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)
& neq(sK54,nil) )
| ( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| sK53 != X6
| ~ ssList(X6) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| sK55 = X4
| ~ ssList(X4) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[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(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X6,X7] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| sK53 != X6
| ~ ssList(X6) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
! [X4,X5] :
( neq(sK54,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ 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(f510,plain,
! [X4,X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f503,f507]) ).
fof(f512,plain,
! [X6,X7] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| sK55 != X6
| ~ ssList(X6) ),
inference(definition_unfolding,[],[f500,f506,f507,f507]) ).
fof(f513,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f514,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f542,plain,
! [X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| ~ ssItem(X5)
| cons(X5,nil) = sK55
| ~ ssList(cons(X5,nil)) ),
inference(equality_resolution,[],[f510]) ).
fof(f543,plain,
( neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f542]) ).
fof(f544,plain,
! [X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| ~ ssItem(X5)
| cons(X5,nil) = sK55
| ~ ssList(cons(X5,nil)) ),
inference(equality_resolution,[],[f502]) ).
fof(f545,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f544]) ).
fof(f548,plain,
! [X7] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X7
| cons(X7,nil) != sK55
| ~ ssItem(X7)
| ~ ssList(sK55) ),
inference(equality_resolution,[],[f512]) ).
fof(f549,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| sK55 != cons(hd(sK56),nil)
| ~ ssItem(hd(sK56))
| ~ ssList(sK55) ),
inference(equality_resolution,[],[f548]) ).
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,[],[f552]) ).
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_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f557]) ).
tcf(c_247,negated_conjecture,
( neq(sK56,nil)
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(cnf_transformation,[],[f543]) ).
tcf(c_248,negated_conjecture,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(cnf_transformation,[],[f545]) ).
tcf(c_250,negated_conjecture,
( ~ ssList(sK55)
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ( cons(hd(sK56),nil) != sK55 ) ),
inference(cnf_transformation,[],[f549]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f513]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f514]) ).
tcf(c_381,plain,
( ~ neq(nil,sK56)
| ( cons(hd(sK56),nil) != sK55 )
| ~ ssItem(hd(sK56)) ),
inference(global_subsumption_just,[status(thm)],[c_250,c_254,c_246,c_250]) ).
tcf(c_382,negated_conjecture,
( ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ( cons(hd(sK56),nil) != sK55 ) ),
inference(renaming,[status(thm)],[c_381]) ).
tcf(c_383,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_247,c_246]) ).
tcf(c_385,plain,
( ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56)) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_246,c_248,c_382]) ).
tcf(c_386,negated_conjecture,
( ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(renaming,[status(thm)],[c_385]) ).
tcf(c_3228,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( X1 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_386]) ).
tcf(c_3229,plain,
( ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(unflattening,[status(thm)],[c_3228]) ).
tcf(c_3230,plain,
( ( nil = sK56 )
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_3229,c_253,c_141,c_3229]) ).
tcf(c_3262,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_383]) ).
tcf(c_3263,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3262]) ).
tcf(c_3264,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3263,c_141,c_3263]) ).
tcf(c_3269,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3230,c_3264]) ).
tcf(c_8873,definition,
iPr_def_10 = hd(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8874,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8876,plain,
( ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3269]) ).
tcf(c_8877,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3264]) ).
tcf(c_8879,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_12179,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8874,c_140]) ).
tcf(c_12182,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12179,c_141]) ).
tcf(c_12192,plain,
~ ssItem(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_12182,c_8876,c_12182]) ).
tcf(c_12308,plain,
( ssItem(iPr_def_10)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8873,c_149]) ).
tcf(c_12310,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12308,c_12192,c_8877,c_8879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC013+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 : n026.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
% 0.10/0.37 % DateTime : Thu Sep 24 15:57:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.70/1.28 % SZS status Started for theBenchmark.p
% 3.70/1.28 % SZS status Theorem for theBenchmark.p
% 3.70/1.28
% 3.70/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.70/1.28
% 3.70/1.28 % ------ iProver source info
% 3.70/1.28
% 3.70/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.70/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.70/1.28 % git: non_committed_changes: false
% 3.70/1.28
% 3.70/1.28 % ------ Parsing...
% 3.70/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.70/1.28
% 3.70/1.28 % ------ 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 %
% 3.70/1.28
% 3.70/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.70/1.28
% 3.70/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.70/1.28 % ------ Proving...
% 3.70/1.28 % ------ Problem Properties
% 3.70/1.28
% 3.70/1.28 %
% 3.70/1.28 % clauses 187
% 3.70/1.28 % conjectures 2
% 3.70/1.28 % EPR 54
% 3.70/1.28 % Horn 119
% 3.70/1.28 % unary 21
% 3.70/1.28 % binary 42
% 3.70/1.28 % lits 627
% 3.70/1.28 % lits eq 82
% 3.70/1.28 % fd_pure 0
% 3.70/1.28 % fd_pseudo 0
% 3.70/1.28 % fd_cond 21
% 3.70/1.28 % fd_pseudo_cond 14
% 3.70/1.28 % AC symbols 0
% 3.70/1.28
% 3.70/1.28 % ------ Schedule dynamic 5 is on
% 3.70/1.28
% 3.70/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.70/1.28
% 3.70/1.28
% 3.70/1.28 % ------
% 3.70/1.28 % Current options:
% 3.70/1.28 % ------
% 3.70/1.28
% 3.70/1.28
% 3.70/1.28 %
% 3.70/1.28
% 3.70/1.28 % ------ Proving...
% 3.70/1.28 %
% 3.70/1.28
% 3.70/1.28 % SZS status Theorem for theBenchmark.p
% 3.70/1.28
% 3.70/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.70/1.28
% 3.70/1.28
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