%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC189+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 : n018.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 03:08:35 PM UTC 2026
% Result : Theorem 2.41s 1.30s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 27 unt; 5 def)
% Number of atoms : 197 ( 64 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 203 ( 75 ~; 66 |; 46 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 57 !; 24 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( X8 = X9
| app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X0 ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X2
& X4 != X5
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| 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)
=> ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( X8 = X9
| app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) != X0 ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X2
& X4 != X5
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X8 != X9
& app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) = X0 ) ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
| X4 = X5
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X8 != X9
& app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) = X0 ) ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
| X4 = X5
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ssItem(sK57)
& ssItem(sK58)
& ssList(sK59)
& ssList(sK60)
& sK57 != sK58
& sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != sK55
| X4 = X5
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ~ ssItem(X4) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X8,sK57),skolemize(X9,sK58),skolemize(X10,sK59),skolemize(X11,sK60)],[f222]) ).
fof(f500,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssList(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK57 != sK58,
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
! [X6,X7,X4,X5] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != sK55
| X4 = X5
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK55 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(definition_unfolding,[],[f505,f507]) ).
tcf(c_246,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ( app(app(app(X0,cons(X1,nil)),cons(X2,nil)),X3) != sK55 ) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_247,negated_conjecture,
app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60) = sK55,
inference(cnf_transformation,[],[f509]) ).
tcf(c_248,negated_conjecture,
sK57 != sK58,
inference(cnf_transformation,[],[f504]) ).
tcf(c_249,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f503]) ).
tcf(c_250,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f502]) ).
tcf(c_251,negated_conjecture,
ssItem(sK58),
inference(cnf_transformation,[],[f501]) ).
tcf(c_252,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f500]) ).
tcf(c_8843,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8844,definition,
iPr_def_11 = app(sK59,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8845,definition,
iPr_def_12 = cons(sK58,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8846,definition,
iPr_def_13 = app(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8847,definition,
iPr_def_14 = app(iPr_def_13,sK60),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_8850,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_8851,negated_conjecture,
ssItem(sK58),
inference(demodulation,[status(thm)],[c_251]) ).
tcf(c_8852,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_8853,negated_conjecture,
ssList(sK60),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8854,negated_conjecture,
sK57 != sK58,
inference(demodulation,[status(thm)],[c_248]) ).
tcf(c_8855,negated_conjecture,
iPr_def_14 = sK55,
inference(demodulation,[status(thm)],[c_247,c_8845,c_8843,c_8844,c_8846,c_8847]) ).
tcf(c_8856,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ( app(app(app(X0,cons(X1,nil)),cons(X2,nil)),X3) != sK55 ) ),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_11705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ( app(app(app(X0,cons(X1,nil)),cons(X2,nil)),X3) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_8856,c_8855]) ).
tcf(c_11712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sK57 )
| ~ ssItem(sK57)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(app(X0,iPr_def_10),cons(X1,nil)),X2) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8843,c_11705]) ).
tcf(c_11720,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sK57 )
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(app(X0,iPr_def_10),cons(X1,nil)),X2) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11712,c_8850]) ).
tcf(c_11806,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK57 )
| ~ ssList(sK59)
| ~ ssList(X1)
| ~ ssItem(X0)
| ( app(app(iPr_def_11,cons(X0,nil)),X1) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8844,c_11720]) ).
tcf(c_11807,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK57 )
| ~ ssList(X1)
| ~ ssItem(X0)
| ( app(app(iPr_def_11,cons(X0,nil)),X1) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11806,c_8852]) ).
tcf(c_11861,plain,
! [X0: $i] :
( ( sK57 = sK58 )
| ~ ssItem(sK58)
| ~ ssList(X0)
| ( app(app(iPr_def_11,iPr_def_12),X0) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8845,c_11807]) ).
tcf(c_11863,plain,
! [X0: $i] :
( ( sK57 = sK58 )
| ~ ssItem(sK58)
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_11861,c_8846]) ).
tcf(c_11864,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11863,c_8854,c_8851]) ).
tcf(c_11947,plain,
~ ssList(sK60),
inference(superposition,[status(thm)],[c_8847,c_11864]) ).
tcf(c_11948,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11947,c_8853]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC189+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 16:55:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 2.41/1.30 % SZS status Started for theBenchmark.p
% 2.41/1.30 % SZS status Theorem for theBenchmark.p
% 2.41/1.30
% 2.41/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.41/1.30
% 2.41/1.30 % ------ iProver source info
% 2.41/1.30
% 2.41/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.41/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.41/1.30 % git: non_committed_changes: false
% 2.41/1.30
% 2.41/1.30 % ------ Parsing...
% 2.41/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.41/1.30
% 2.41/1.30 % ------ 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: 4 0s sf_e pe_s pe_e %
% 2.41/1.30
% 2.41/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.41/1.30
% 2.41/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.41/1.30 % ------ Proving...
% 2.41/1.30 % ------ Problem Properties
% 2.41/1.30
% 2.41/1.30 %
% 2.41/1.30 % clauses 194
% 2.41/1.30 % conjectures 9
% 2.41/1.30 % EPR 57
% 2.41/1.30 % Horn 126
% 2.41/1.30 % unary 29
% 2.41/1.30 % binary 40
% 2.41/1.30 % lits 637
% 2.41/1.30 % lits eq 87
% 2.41/1.30 % fd_pure 0
% 2.41/1.30 % fd_pseudo 0
% 2.41/1.30 % fd_cond 21
% 2.41/1.30 % fd_pseudo_cond 15
% 2.41/1.30 % AC symbols 0
% 2.41/1.30
% 2.41/1.30 % ------ Schedule dynamic 5 is on
% 2.41/1.30
% 2.41/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.30
% 2.41/1.30
% 2.41/1.30 % ------
% 2.41/1.30 % Current options:
% 2.41/1.30 % ------
% 2.41/1.30
% 2.41/1.30
% 2.41/1.30 %
% 2.41/1.30
% 2.41/1.30 % ------ Proving...
% 2.41/1.30 %
% 2.41/1.30
% 2.41/1.30 % SZS status Theorem for theBenchmark.p
% 2.41/1.30
% 2.41/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/1.30
% 3.94/1.30
%------------------------------------------------------------------------------