%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT058-1 : 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 02:40:40 PM UTC 2026
% Result : Unsatisfiable 7.61s 6.94s
% Output : CNFRefutation 7.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 38 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-5 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f663,axiom,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2)))
| hBOOL(c_in(c_Pair(X0,X1,X2,X3),hAPP(c_Relation_Oconverse(X3,X2),X4),tc_prod(X2,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
fof(f664,axiom,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(c_Pair(X1,X0,X3,X2),hAPP(c_Relation_Oconverse(X2,X3),X4),tc_prod(X3,X2)))
| hBOOL(c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
fof(f672,axiom,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),X5) = hAPP(X0,hAPP(X1,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
fof(f676,axiom,
! [X0] :
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f677,axiom,
! [X0] :
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f683,negated_conjecture,
( hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f684,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tcf(c_1273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(c_in(c_Pair(X1,X0,X3,X2),hAPP(c_Relation_Oconverse(X2,X3),X4),tc_prod(X3,X2)))
| ~ hBOOL(c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))) ),
inference(cnf_transformation,[],[f663]) ).
tcf(c_1274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2)))
| ~ hBOOL(c_in(c_Pair(X0,X1,X2,X3),hAPP(c_Relation_Oconverse(X3,X2),X4),tc_prod(X2,X3))) ),
inference(cnf_transformation,[],[f664]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),X5) = hAPP(X0,hAPP(X1,X5)),
inference(cnf_transformation,[],[f672]) ).
tcf(c_1286,plain,
! [X0: $i] :
( hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnf_transformation,[],[f676]) ).
tcf(c_1287,plain,
! [X0: $i] :
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnf_transformation,[],[f677]) ).
tcf(c_1293,negated_conjecture,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnf_transformation,[],[f683]) ).
tcf(c_1294,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnf_transformation,[],[f684]) ).
tcf(c_1582,plain,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(demodulation,[status(thm)],[c_1293,c_1282]) ).
tcf(c_1588,plain,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_1582,c_1274]) ).
tcf(c_1609,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(demodulation,[status(thm)],[c_1294,c_1282]) ).
tcf(c_1615,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_1273,c_1609]) ).
tcf(c_3973,plain,
hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(forward_subsumption_resolution,[status(thm)],[c_1588,c_1287]) ).
tcf(c_3975,plain,
hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(superposition,[status(thm)],[c_3973,c_1286]) ).
tcf(c_3979,plain,
~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(global_subsumption_just,[status(thm)],[c_1615,c_1615,c_3975]) ).
tcf(c_3981,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3979,c_3973]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT058-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/5.45 % Computer : n004.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Thu Sep 24 08:39:31 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/5.51 Running first-order theorem proving
% 0.22/5.51 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
% 0.22/5.53
% 0.22/5.53 % ======== iProver multi-core TPTP/SMT =========
% 0.22/5.53
% 0.22/5.53 % Detected problem language: tptp
% 0.22/5.54 % Proving...
% 7.61/6.94 % SZS status Started for theBenchmark.p
% 7.61/6.94 % SZS status Unsatisfiable for theBenchmark.p
% 7.61/6.94
% 7.61/6.94 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.61/6.94
% 7.61/6.94 % ------ iProver source info
% 7.61/6.94
% 7.61/6.94 % git: date: 2026-07-19 20:42:38 +0200
% 7.61/6.94 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.61/6.94 % git: non_committed_changes: false
% 7.61/6.94
% 7.61/6.94 % ------ Parsing...% successful
% 7.61/6.94
% 7.61/6.94
% 7.61/6.94 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.61/6.94 % ------ Proving...
% 7.61/6.94 % ------ Problem Properties
% 7.61/6.94
% 7.61/6.94 %
% 7.61/6.94 % clauses 627
% 7.61/6.94 % conjectures 2
% 7.61/6.94 % EPR 33
% 7.61/6.94 % Horn 553
% 7.61/6.94 % unary 175
% 7.61/6.94 % binary 254
% 7.61/6.94 % lits 1341
% 7.61/6.94 % lits eq 285
% 7.61/6.94 % fd_pure 0
% 7.61/6.94 % fd_pseudo 0
% 7.61/6.94 % fd_cond 0
% 7.61/6.94 % fd_pseudo_cond 53
% 7.61/6.94 % AC symbols 0
% 7.61/6.94
% 7.61/6.94 % ------ Input Options Time Limit: Unbounded
% 7.61/6.94
% 7.61/6.94
% 7.61/6.94 % ------
% 7.61/6.94 % Current options:
% 7.61/6.94 % ------
% 7.61/6.94
% 7.61/6.94
% 7.61/6.94 %
% 7.61/6.94
% 7.61/6.94 % ------ Proving...
% 7.61/6.94 %
% 7.61/6.94
% 7.61/6.94 % SZS status Unsatisfiable for theBenchmark.p
% 7.61/6.94
% 7.61/6.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.61/6.94
% 7.61/6.94
%------------------------------------------------------------------------------