%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC313-1 : 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 : n009.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 03:09:16 PM UTC 2026
% Result : Unsatisfiable 7.63s 4.39s
% Output : CNFRefutation 7.63s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f246ERROR: Could not build tree for root c_30161ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause9) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
fof(f83,axiom,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
fof(f84,axiom,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f112,axiom,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
fof(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/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(f193,axiom,
! [X2,X3,X0,X1,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0,X1] :
( app(cons(X0,nil),X1) != sk4
| app(X1,cons(X0,nil)) = sk3
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) != sk4
| sk3 = app(X1,cons(X0,nil))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
! [X0,X1] :
( app(X1,cons(X0,nil)) != sk1
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,plain,
! [X0,X1] :
( sk1 != app(X1,cons(X0,nil))
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil = sk2 ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
! [X0,X1] :
( app(X1,cons(X0,nil)) != sk1
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
! [X0,X1] :
( sk1 != app(X1,cons(X0,nil))
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != sk1 ),
inference(reorient_equations,[],[f213]) ).
fof(f217,plain,
( neq(sk4,nil)
| nil = sk4 ),
inference(definition_unfolding,[],[f209,f204,f204]) ).
fof(f218,plain,
! [X0,X1] :
( sk3 != app(X1,cons(X0,nil))
| app(cons(X0,nil),X1) != sk4
| ~ ssList(X1)
| ~ ssItem(X0)
| nil = sk4 ),
inference(definition_unfolding,[],[f211,f204,f204,f205]) ).
fof(f219,plain,
( neq(sk4,nil)
| nil != sk3 ),
inference(definition_unfolding,[],[f212,f205,f204]) ).
fof(f220,plain,
! [X0,X1] :
( sk3 != app(X1,cons(X0,nil))
| app(cons(X0,nil),X1) != sk4
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != sk3 ),
inference(definition_unfolding,[],[f214,f205,f204,f205]) ).
fof(f223,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f238,plain,
! [X2,X3,X0,X1] :
( ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_resolution,[],[f193]) ).
tcf(c_253,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_254,plain,
ssItem(skac3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_258,plain,
! [X0: $i] : ssList(skaf82(X0)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_328,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_329,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_354,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_424,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_433,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_434,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_435,negated_conjecture,
! [X0: $i,X1: $i] :
( ( app(X1,cons(X0,nil)) = sk3 )
| ~ ssItem(X0)
| ~ ssList(X1)
| ( app(cons(X0,nil),X1) != sk4 ) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_436,negated_conjecture,
( ( sk3 = nil )
| ( sk4 != nil ) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_437,negated_conjecture,
( neq(sk4,nil)
| ( sk4 = nil ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_438,negated_conjecture,
! [X0: $i,X1: $i] :
( ( sk4 = nil )
| ~ ssItem(X0)
| ~ ssList(X1)
| ( app(X1,cons(X0,nil)) != sk3 )
| ( app(cons(X0,nil),X1) != sk4 ) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_439,negated_conjecture,
( neq(sk4,nil)
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_440,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( sk3 != nil )
| ( app(X1,cons(X0,nil)) != sk3 )
| ( app(cons(X0,nil),X1) != sk4 ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_486,plain,
( ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(instantiation,[status(thm)],[c_360]) ).
tcf(c_501,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_329]) ).
tcf(c_557,negated_conjecture,
neq(sk4,nil),
inference(global_subsumption_just,[status(thm)],[c_437,c_437,c_439,c_436]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) != sk4 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_435,c_436,c_435,c_438,c_440]) ).
tcf(c_568,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( app(cons(X0,nil),X1) != sk4 ) ),
inference(renaming,[status(thm)],[c_567]) ).
tcf(c_572,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( app(cons(X0,nil),X1) != sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_440,c_568]) ).
tcf(c_712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( neq(X0,X2)
| ~ neq(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2388,plain,
( ( sk4 = nil )
| ( cons(skaf83(sk4),skaf82(sk4)) = sk4 )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_2545,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ~ neq(sk4,nil)
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(instantiation,[status(thm)],[c_717]) ).
tcf(c_2546,plain,
( neq(nil,nil)
| ~ neq(sk4,nil)
| ( nil != nil )
| ( nil != sk4 ) ),
inference(instantiation,[status(thm)],[c_2545]) ).
tcf(c_3328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(X4)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(resolution,[status(thm)],[c_424,c_317]) ).
tcf(c_3465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(X4)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(cons(X1,X3))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[c_3328,c_330]) ).
tcf(c_3485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(X4)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3465,c_331]) ).
tcf(c_3504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(X4)
| ~ ssItem(X0)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[c_3485,c_330]) ).
tcf(c_3511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3504,c_331]) ).
tcf(c_3533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c_3511,c_254]) ).
tcf(c_3613,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c_3533,c_433]) ).
tcf(c_4098,plain,
! [X0: $i,X1: $i] :
( ssItem(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c_3613,c_433]) ).
tcf(c_4142,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_365,c_4098]) ).
tcf(c_4173,plain,
! [X0: $i] : ssItem(X0),
inference(resolution,[status(thm)],[c_4098,c_433]) ).
tcf(c_8321,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk4 )
| ( sk4 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_712]) ).
tcf(c_8322,plain,
( ( nil = sk4 )
| ( nil != nil )
| ( sk4 != nil ) ),
inference(instantiation,[status(thm)],[c_8321]) ).
tcf(c_28021,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) != sk4 )
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_572,c_568,c_4173]) ).
tcf(c_28022,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ( app(cons(X0,nil),X1) != sk4 ) ),
inference(renaming,[status(thm)],[c_28021]) ).
tcf(c_29195,plain,
( ( sk4 = nil )
| ( cons(skaf83(sk4),skaf82(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_434,c_354]) ).
tcf(c_29227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_365,c_4142]) ).
tcf(c_29232,plain,
! [X0: $i,X1: $i] : app(cons(X0,nil),skaf82(X1)) = cons(X0,skaf82(X1)),
inference(superposition,[status(thm)],[c_258,c_29227]) ).
tcf(c_29466,plain,
cons(skaf83(sk4),skaf82(sk4)) = sk4,
inference(global_subsumption_just,[status(thm)],[c_29195,c_434,c_253,c_328,c_486,c_501,c_557,c_2388,c_2546,c_8322]) ).
tcf(c_29559,plain,
! [X0: $i,X1: $i] :
( ~ ssList(skaf82(X1))
| ( cons(X0,skaf82(X1)) != sk4 ) ),
inference(superposition,[status(thm)],[c_29232,c_28022]) ).
tcf(c_29571,plain,
~ ssList(skaf82(sk4)),
inference(superposition,[status(thm)],[c_29466,c_29559]) ).
tcf(c_30161,plain,
$false,
inference(superposition,[status(thm)],[c_258,c_29571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC313-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.57 % Computer : n009.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Thu Sep 24 17:34:30 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.61 Running first-order theorem proving
% 0.10/0.61 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
% 0.10/0.63
% 0.10/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.63
% 0.10/0.63 % Detected problem language: tptp
% 0.13/0.64 % Proving...
% 7.63/4.39 % SZS status Started for theBenchmark.p
% 7.63/4.39 % SZS status Unsatisfiable for theBenchmark.p
% 7.63/4.39
% 7.63/4.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.63/4.39
% 7.63/4.39 % ------ iProver source info
% 7.63/4.39
% 7.63/4.39 % git: date: 2026-07-19 20:42:38 +0200
% 7.63/4.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.63/4.39 % git: non_committed_changes: false
% 7.63/4.39
% 7.63/4.39 % ------ Parsing...% successful
% 7.63/4.39
% 7.63/4.39
% 7.63/4.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.63/4.39
% 7.63/4.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 7.63/4.39
% 7.63/4.39 % ------ Preprocessing...%
% 7.63/4.39
% 7.63/4.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.63/4.39 % ------ Proving...
% 7.63/4.39 % ------ Problem Properties
% 7.63/4.39
% 7.63/4.39 %
% 7.63/4.39 % clauses 184
% 7.63/4.39 % conjectures 17
% 7.63/4.39 % EPR 58
% 7.63/4.39 % Horn 154
% 7.63/4.39 % unary 61
% 7.63/4.39 % binary 22
% 7.63/4.39 % lits 559
% 7.63/4.39 % lits eq 74
% 7.63/4.39 % fd_pure 0
% 7.63/4.39 % fd_pseudo 0
% 7.63/4.39 % fd_cond 15
% 7.63/4.39 % fd_pseudo_cond 16
% 7.63/4.39 % AC symbols 0
% 7.63/4.39
% 7.63/4.39 % ------ Input Options Time Limit: Unbounded
% 7.63/4.39
% 7.63/4.39
% 7.63/4.39 % ------
% 7.63/4.39 % Current options:
% 7.63/4.39 % ------
% 7.63/4.39
% 7.63/4.39
% 7.63/4.39 %
% 7.63/4.39
% 7.63/4.39 % ------ Proving...
% 7.63/4.39 %
% 7.63/4.39
% 7.63/4.39 % SZS status Unsatisfiable for theBenchmark.p
% 7.63/4.39
% 7.63/4.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.63/4.39
% 7.63/4.39
%------------------------------------------------------------------------------