%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT023-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 02:40:37 PM UTC 2026
% Result : Unsatisfiable 22.04s 9.52s
% Output : CNFRefutation 22.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 57 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 18 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f635,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Otrans(X3,X2)
| ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transD_0) ).
fof(f640,negated_conjecture,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f641,negated_conjecture,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f642,negated_conjecture,
! [X0] : ~ c_in(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f643,negated_conjecture,
~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f644,negated_conjecture,
! [X2,X0,X1] :
( X1 = X0
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f645,plain,
! [X2,X0,X1] :
( X0 = X1
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(reorient_equations,[],[f644]) ).
fof(f648,negated_conjecture,
! [X0,X1] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X3,X2)
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f635]) ).
tcf(c_1219,negated_conjecture,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[],[f640]) ).
tcf(c_1220,negated_conjecture,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[],[f641]) ).
tcf(c_1221,negated_conjecture,
! [X0: $i] : ~ c_in(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[],[f642]) ).
tcf(c_1222,negated_conjecture,
~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[],[f643]) ).
tcf(c_1223,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f645]) ).
tcf(c_1225,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f648]) ).
tcf(c_1399,plain,
( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( v_a = v_b ) ),
inference(superposition,[status(thm)],[c_1223,c_1222]) ).
tcf(c_1411,plain,
! [X0: $i] :
( c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(superposition,[status(thm)],[c_1219,c_1214]) ).
tcf(c_1564,plain,
( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( v_a = v_b ) ),
inference(superposition,[status(thm)],[c_1223,c_1222]) ).
tcf(c_1573,plain,
( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( v_a = v_b ) ),
inference(superposition,[status(thm)],[c_1399,c_1225]) ).
tcf(c_1583,plain,
! [X0: $i] :
( c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(superposition,[status(thm)],[c_1219,c_1214]) ).
tcf(c_1608,plain,
! [X0: $i] :
( c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(global_subsumption_just,[status(thm)],[c_1411,c_1220,c_1411]) ).
tcf(c_1856,plain,
( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( v_a = v_b ) ),
inference(superposition,[status(thm)],[c_1564,c_1225]) ).
tcf(c_1877,plain,
! [X0: $i] :
( c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(global_subsumption_just,[status(thm)],[c_1583,c_1220,c_1411]) ).
tcf(c_2406,plain,
( c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( v_a = v_b ) ),
inference(superposition,[status(thm)],[c_1573,c_1608]) ).
tcf(c_3426,plain,
( c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( v_a = v_b ) ),
inference(superposition,[status(thm)],[c_1856,c_1877]) ).
tcf(c_25110,plain,
v_a = v_b,
inference(forward_subsumption_resolution,[status(thm)],[c_2406,c_1221]) ).
tcf(c_25116,plain,
c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(superposition,[status(thm)],[c_25110,c_1219]) ).
tcf(c_46157,plain,
c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(global_subsumption_just,[status(thm)],[c_3426,c_25116]) ).
tcf(c_46159,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_46157,c_1221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT023-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.60 % Computer : n004.cluster.edu
% 0.13/5.60 % Model : x86_64 x86_64
% 0.13/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.60 % Memory : 8046.5625MB
% 0.13/5.60 % OS : Linux 6.8.0-71-generic
% 0.13/5.60 % CPULimit : 300
% 0.13/5.60 % WCLimit : 300
% 0.13/5.60 % DateTime : Thu Sep 24 08:34:28 UTC 2026
% 0.13/5.60 % CPUTime :
% 0.13/5.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.63 Running first-order theorem proving
% 0.13/5.63 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
% 0.13/5.65
% 0.13/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.65
% 0.13/5.65 % Detected problem language: tptp
% 0.13/5.66 % Proving...
% 22.04/9.52 % SZS status Started for theBenchmark.p
% 22.04/9.52 % SZS status Unsatisfiable for theBenchmark.p
% 22.04/9.52
% 22.04/9.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.04/9.52
% 22.04/9.52 % ------ iProver source info
% 22.04/9.52
% 22.04/9.52 % git: date: 2026-07-19 20:42:38 +0200
% 22.04/9.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.04/9.52 % git: non_committed_changes: false
% 22.04/9.52
% 22.04/9.52 % ------ Parsing...% successful
% 22.04/9.52
% 22.04/9.52
% 22.04/9.52 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 22.04/9.52 % ------ Proving...
% 22.04/9.52 % ------ Problem Properties
% 22.04/9.52
% 22.04/9.52 %
% 22.04/9.52 % clauses 592
% 22.04/9.52 % conjectures 9
% 22.04/9.52 % EPR 26
% 22.04/9.52 % Horn 534
% 22.04/9.52 % unary 171
% 22.04/9.52 % binary 239
% 22.04/9.52 % lits 1241
% 22.04/9.52 % lits eq 255
% 22.04/9.52 % fd_pure 0
% 22.04/9.52 % fd_pseudo 0
% 22.04/9.52 % fd_cond 0
% 22.04/9.52 % fd_pseudo_cond 50
% 22.04/9.52 % AC symbols 0
% 22.04/9.52
% 22.04/9.52 % ------ Input Options Time Limit: Unbounded
% 22.04/9.52
% 22.04/9.52
% 22.04/9.52 % ------
% 22.04/9.52 % Current options:
% 22.04/9.52 % ------
% 22.04/9.52
% 22.04/9.52
% 22.04/9.52 %
% 22.04/9.52
% 22.04/9.52 % ------ Proving...
% 22.04/9.52 %
% 22.04/9.52
% 22.04/9.52 % SZS status Unsatisfiable for theBenchmark.p
% 22.04/9.52
% 22.04/9.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.04/9.52
% 22.04/9.52
%------------------------------------------------------------------------------