%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% 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 02:40:37 PM UTC 2026
% Result : Unsatisfiable 10.30s 7.71s
% Output : CNFRefutation 10.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 19 unt; 0 def)
% Number of atoms : 54 ( 8 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f292,axiom,
! [X2,X0,X1] : hBOOL(c_in(X0,hAPP(c_Set_Oinsert(X0,X1),X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
fof(f300,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X2,X1))
| hAPP(c_Set_Oinsert(X0,X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f767,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Oirrefl(X2,X1)
| ~ hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f774,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f775,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f776,negated_conjecture,
! [X0] : c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f777,negated_conjecture,
! [X0] : c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f778,negated_conjecture,
! [X0] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f779,negated_conjecture,
hBOOL(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/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f780,negated_conjecture,
~ hBOOL(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/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f784,negated_conjecture,
! [X2,X0,X1] :
( ~ c_Relation_Otrans(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1
| ~ hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
tcf(c_764,negated_conjecture,
! [X0: $i] : c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[],[f776]) ).
tcf(c_765,negated_conjecture,
! [X0: $i] : c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[],[f777]) ).
tcf(c_766,negated_conjecture,
! [X0: $i] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[],[f778]) ).
tcf(c_767,negated_conjecture,
hBOOL(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,[],[f779]) ).
tcf(c_768,negated_conjecture,
~ hBOOL(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,[],[f780]) ).
tcf(c_772,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( X0 = X1 )
| ~ c_Relation_Otrans(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnf_transformation,[],[f784]) ).
tcf(c_784,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Relation_Oirrefl(X2,X1)
| ~ hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))) ),
inference(cnf_transformation,[],[f767]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[],[f775]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(c_in(X1,X0,X2))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f774]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Set_Oinsert(X0,X2),X1) = X1 )
| ~ hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i,X2: $i] : hBOOL(c_in(X0,hAPP(c_Set_Oinsert(X0,X1),X2),X1)),
inference(cnf_transformation,[],[f292]) ).
tcf(c_17144,plain,
( hBOOL(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)))
| ( v_a = v_b )
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(superposition,[status(thm)],[c_767,c_772]) ).
tcf(c_17145,plain,
v_a = v_b,
inference(forward_subsumption_resolution,[status(thm)],[c_17144,c_768,c_764,c_765,c_766]) ).
tcf(c_17147,plain,
hBOOL(c_in(c_Pair(v_a,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))),
inference(demodulation,[status(thm)],[c_767,c_17145]) ).
tcf(c_17321,plain,
hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(superposition,[status(thm)],[c_17147,c_805]) ).
tcf(c_19133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Set_Oinsert(X1,X2),X0) = X0 )
| ~ hBOOL(hAPP(X0,X1)) ),
inference(superposition,[status(thm)],[c_806,c_1126]) ).
tcf(c_19584,plain,
! [X0: $i] : hAPP(c_Set_Oinsert(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),hAPP(v_P,v_i)) = hAPP(v_P,v_i),
inference(superposition,[status(thm)],[c_17321,c_19133]) ).
tcf(c_19798,plain,
! [X0: $i] : hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X0)),
inference(superposition,[status(thm)],[c_19584,c_1130]) ).
tcf(c_21492,plain,
~ c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),
inference(superposition,[status(thm)],[c_19798,c_784]) ).
tcf(c_21495,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21492,c_765]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.79 % Computer : n013.cluster.edu
% 0.10/5.79 % Model : x86_64 x86_64
% 0.10/5.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.79 % Memory : 8046.5625MB
% 0.10/5.79 % OS : Linux 6.8.0-71-generic
% 0.10/5.79 % CPULimit : 300
% 0.10/5.79 % WCLimit : 300
% 0.10/5.79 % DateTime : Thu Sep 24 08:33:58 UTC 2026
% 0.10/5.79 % CPUTime :
% 0.10/5.79 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.83 Running first-order theorem proving
% 0.15/5.83 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
% 0.15/5.84
% 0.15/5.84 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.84
% 0.15/5.84 % Detected problem language: tptp
% 0.15/5.86 % Proving...
% 10.30/7.71 % SZS status Started for theBenchmark.p
% 10.30/7.71 % SZS status Unsatisfiable for theBenchmark.p
% 10.30/7.71
% 10.30/7.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.30/7.71
% 10.30/7.71 % ------ iProver source info
% 10.30/7.71
% 10.30/7.71 % git: date: 2026-07-19 20:42:38 +0200
% 10.30/7.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.30/7.71 % git: non_committed_changes: false
% 10.30/7.71
% 10.30/7.71 % ------ Parsing...% successful
% 10.30/7.71
% 10.30/7.71
% 10.30/7.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.30/7.71
% 10.30/7.71 % ------ Preprocessing... sup_sim: 32 sf_s rm: 18 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 10.30/7.71
% 10.30/7.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.30/7.71
% 10.30/7.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.30/7.71 % ------ Proving...
% 10.30/7.71 % ------ Problem Properties
% 10.30/7.71
% 10.30/7.71 %
% 10.30/7.71 % clauses 395
% 10.30/7.71 % conjectures 9
% 10.30/7.71 % EPR 6
% 10.30/7.71 % Horn 371
% 10.30/7.71 % unary 149
% 10.30/7.71 % binary 147
% 10.30/7.71 % lits 757
% 10.30/7.71 % lits eq 209
% 10.30/7.71 % fd_pure 0
% 10.30/7.71 % fd_pseudo 0
% 10.30/7.71 % fd_cond 0
% 10.30/7.71 % fd_pseudo_cond 28
% 10.30/7.71 % AC symbols 0
% 10.30/7.71
% 10.30/7.71 % ------ Schedule dynamic 5 is on
% 10.30/7.71
% 10.30/7.71 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.30/7.71
% 10.30/7.71
% 10.30/7.71 % ------
% 10.30/7.71 % Current options:
% 10.30/7.71 % ------
% 10.30/7.71
% 10.30/7.71
% 10.30/7.71 %
% 10.30/7.71
% 10.30/7.71 % ------ Proving...
% 10.30/7.71 %
% 10.30/7.71
% 10.30/7.71 % SZS status Unsatisfiable for theBenchmark.p
% 10.30/7.71
% 10.30/7.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.30/7.71
% 10.30/7.71
%------------------------------------------------------------------------------