%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC419-1 : 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 : n013.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 03:09:49 PM UTC 2026
% Result : Unsatisfiable 3.01s 1.29s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 56 ( 27 unt; 3 def)
% Number of atoms : 157 ( 45 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 137 ( 75 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X2,X0,X1] :
( app(app(X2,cons(X0,nil)),X1) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
! [X2,X0,X1] :
( sk1 != app(app(X2,cons(X0,nil)),X1)
| sk2 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f207]) ).
fof(f210,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f211,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f213,plain,
( ~ neq(sk4,nil)
| sk4 = app(cons(sk5,nil),sk6) ),
inference(reorient_equations,[],[f212]) ).
fof(f214,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f215,plain,
( ~ neq(sk4,nil)
| sk3 = app(sk6,cons(sk5,nil)) ),
inference(reorient_equations,[],[f214]) ).
fof(f218,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f219,plain,
! [X2,X0,X1] :
( sk3 != app(app(X2,cons(X0,nil)),X1)
| sk4 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f208,f204,f205]) ).
tcf(c_254,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_319,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_320,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_434,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_436,negated_conjecture,
neq(sk4,nil),
inference(cnf_transformation,[],[f218]) ).
tcf(c_437,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != sk4 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_439,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_440,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_441,negated_conjecture,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_442,negated_conjecture,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_551,negated_conjecture,
ssList(sk6),
inference(global_subsumption_just,[status(thm)],[c_440,c_436,c_440]) ).
tcf(c_553,negated_conjecture,
ssItem(sk5),
inference(global_subsumption_just,[status(thm)],[c_439,c_436,c_439]) ).
tcf(c_567,negated_conjecture,
app(sk6,cons(sk5,nil)) = sk3,
inference(global_subsumption_just,[status(thm)],[c_442,c_436,c_442]) ).
tcf(c_569,negated_conjecture,
app(cons(sk5,nil),sk6) = sk4,
inference(global_subsumption_just,[status(thm)],[c_441,c_436,c_441]) ).
tcf(c_6512,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6513,definition,
iPr_def_13 = app(iPr_def_12,sk6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6514,definition,
iPr_def_14 = app(sk6,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6516,negated_conjecture,
iPr_def_13 = sk4,
inference(demodulation,[status(thm)],[c_569,c_6512,c_6513]) ).
tcf(c_6517,negated_conjecture,
iPr_def_14 = sk3,
inference(demodulation,[status(thm)],[c_567,c_6514]) ).
tcf(c_6518,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_553]) ).
tcf(c_6519,negated_conjecture,
ssList(sk6),
inference(demodulation,[status(thm)],[c_551]) ).
tcf(c_6520,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != sk4 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(demodulation,[status(thm)],[c_437]) ).
tcf(c_6522,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_434]) ).
tcf(c_9048,plain,
ssList(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_6522,c_6517]) ).
tcf(c_9049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != iPr_def_13 )
| ( app(app(X0,cons(X1,nil)),X2) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6520,c_6516,c_6517]) ).
tcf(c_9060,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(sk5)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_12),X0) != iPr_def_14 )
| ( app(app(X0,cons(sk5,nil)),X1) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6512,c_9049]) ).
tcf(c_9061,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(sk5)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_12),X0) != iPr_def_14 )
| ( app(app(X0,iPr_def_12),X1) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_9060,c_6512]) ).
tcf(c_9062,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_12),X0) != iPr_def_14 )
| ( app(app(X0,iPr_def_12),X1) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9061,c_6518]) ).
tcf(c_9076,plain,
! [X0: $i] :
( ~ ssList(sk6)
| ~ ssList(X0)
| ( app(iPr_def_14,X0) != iPr_def_14 )
| ( app(app(X0,iPr_def_12),sk6) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6514,c_9062]) ).
tcf(c_9077,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(iPr_def_14,X0) != iPr_def_14 )
| ( app(app(X0,iPr_def_12),sk6) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9076,c_6519]) ).
tcf(c_9202,plain,
app(iPr_def_14,nil) = iPr_def_14,
inference(superposition,[status(thm)],[c_9048,c_319]) ).
tcf(c_9505,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6512,c_332]) ).
tcf(c_9509,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9505,c_6518,c_254]) ).
tcf(c_9522,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_9509,c_320]) ).
tcf(c_9537,plain,
( ~ ssList(nil)
| ( app(iPr_def_14,nil) != iPr_def_14 )
| ( app(iPr_def_12,sk6) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9522,c_9077]) ).
tcf(c_9539,plain,
~ ssList(nil),
inference(ground_joinability,[status(thm)],[c_9537,c_6513,c_9202]) ).
tcf(c_9540,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9539,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC419-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 18:08:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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...
% 3.01/1.29 % SZS status Started for theBenchmark.p
% 3.01/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.01/1.29
% 3.01/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.01/1.29
% 3.01/1.29 % ------ iProver source info
% 3.01/1.29
% 3.01/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.01/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.01/1.29 % git: non_committed_changes: false
% 3.01/1.29
% 3.01/1.29 % ------ Parsing...% successful
% 3.01/1.29
% 3.01/1.29
% 3.01/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.01/1.29
% 3.01/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.01/1.29
% 3.01/1.29 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.01/1.29
% 3.01/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.01/1.29 % ------ Proving...
% 3.01/1.29 % ------ Problem Properties
% 3.01/1.29
% 3.01/1.29 %
% 3.01/1.29 % clauses 188
% 3.01/1.29 % conjectures 7
% 3.01/1.29 % EPR 59
% 3.01/1.29 % Horn 160
% 3.01/1.29 % unary 68
% 3.01/1.29 % binary 21
% 3.01/1.29 % lits 556
% 3.01/1.29 % lits eq 77
% 3.01/1.29 % fd_pure 0
% 3.01/1.29 % fd_pseudo 0
% 3.01/1.29 % fd_cond 15
% 3.01/1.29 % fd_pseudo_cond 14
% 3.01/1.29 % AC symbols 0
% 3.01/1.29
% 3.01/1.29 % ------ Schedule dynamic 5 is on
% 3.01/1.29
% 3.01/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.01/1.29
% 3.01/1.29
% 3.01/1.29 % ------
% 3.01/1.29 % Current options:
% 3.01/1.29 % ------
% 3.01/1.29
% 3.01/1.29
% 3.01/1.29 %
% 3.01/1.29
% 3.01/1.29 % ------ Proving...
% 3.01/1.29 %
% 3.01/1.29
% 3.01/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.01/1.29
% 3.01/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.01/1.29
% 3.01/1.29
%------------------------------------------------------------------------------