%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET825-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 02:48:40 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.27s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 17 unt; 3 def)
% Number of atoms : 83 ( 12 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 43 ( 22 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f3,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f4,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f5,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,negated_conjecture,
v_Q(v_n),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,negated_conjecture,
~ v_Q(v_m),
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_109,plain,
v_n != v_m,
inference(resolution_lifted,[status(thm)],[c_57,c_58]) ).
tcf(c_155,definition,
iPr_def_10 = tc_prod(tc_nat,tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_156,definition,
iPr_def_11 = c_Pair(c_0,c_0,tc_nat,tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_157,definition,
iPr_def_12 = c_Pair(v_n,v_m,tc_nat,tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_158,plain,
v_n != v_m,
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_159,negated_conjecture,
! [X0: $i] :
( c_in(iPr_def_12,X0,iPr_def_10)
| ~ c_in(iPr_def_11,X0,iPr_def_10)
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_60,c_157,c_156,c_155]) ).
tcf(c_160,negated_conjecture,
! [X0: $i] :
( c_in(iPr_def_12,X0,iPr_def_10)
| c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,iPr_def_10)
| ~ c_in(iPr_def_11,X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_314,plain,
c_in(iPr_def_11,c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(superposition,[status(thm)],[c_156,c_55]) ).
tcf(c_315,plain,
! [X0: $i] : c_in(c_Pair(X0,X0,tc_nat,tc_nat),c_Relation_OId,iPr_def_10),
inference(superposition,[status(thm)],[c_155,c_55]) ).
tcf(c_316,plain,
c_in(iPr_def_11,c_Relation_OId,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_314,c_155]) ).
tcf(c_324,plain,
( ( v_n = v_m )
| ~ c_in(iPr_def_12,c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(superposition,[status(thm)],[c_157,c_56]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,tc_nat,tc_nat),c_Relation_OId,iPr_def_10) ),
inference(superposition,[status(thm)],[c_155,c_56]) ).
tcf(c_327,plain,
( ( v_n = v_m )
| ~ c_in(iPr_def_12,c_Relation_OId,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_324,c_155]) ).
tcf(c_328,plain,
~ c_in(iPr_def_12,c_Relation_OId,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_327,c_158]) ).
tcf(c_335,plain,
( c_in(iPr_def_12,c_Relation_OId,iPr_def_10)
| ( v_x(c_Relation_OId) = v_xa(c_Relation_OId) )
| ~ c_in(iPr_def_11,c_Relation_OId,iPr_def_10) ),
inference(superposition,[status(thm)],[c_160,c_326]) ).
tcf(c_339,plain,
v_x(c_Relation_OId) = v_xa(c_Relation_OId),
inference(forward_subsumption_resolution,[status(thm)],[c_335,c_328,c_316]) ).
tcf(c_340,plain,
( c_in(iPr_def_12,c_Relation_OId,iPr_def_10)
| ~ c_in(iPr_def_11,c_Relation_OId,iPr_def_10)
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,iPr_def_10) ),
inference(superposition,[status(thm)],[c_339,c_159]) ).
tcf(c_342,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_340,c_328,c_316,c_315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET825-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n001.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 12:10:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.66/1.27 % SZS status Started for theBenchmark.p
% 1.66/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.27
% 1.66/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.66/1.27
% 1.66/1.27 % ------ iProver source info
% 1.66/1.27
% 1.66/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.66/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.66/1.27 % git: non_committed_changes: false
% 1.66/1.27
% 1.66/1.27 % ------ Parsing...% successful
% 1.66/1.27
% 1.66/1.27
% 1.66/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.66/1.27
% 1.66/1.27 % ------ 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 %
% 1.66/1.27
% 1.66/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.66/1.27
% 1.66/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.66/1.27 % ------ Proving...
% 1.66/1.27 % ------ Problem Properties
% 1.66/1.27
% 1.66/1.27 %
% 1.66/1.27 % clauses 8
% 1.66/1.27 % conjectures 2
% 1.66/1.27 % EPR 1
% 1.66/1.27 % Horn 7
% 1.66/1.27 % unary 5
% 1.66/1.27 % binary 1
% 1.66/1.27 % lits 13
% 1.66/1.27 % lits eq 5
% 1.66/1.27 % fd_pure 0
% 1.66/1.27 % fd_pseudo 0
% 1.66/1.27 % fd_cond 0
% 1.66/1.27 % fd_pseudo_cond 1
% 1.66/1.27 % AC symbols 0
% 1.66/1.27
% 1.66/1.27 % ------ Schedule dynamic 5 is on
% 1.66/1.27
% 1.66/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.66/1.27
% 1.66/1.27
% 1.66/1.27 % ------
% 1.66/1.27 % Current options:
% 1.66/1.27 % ------
% 1.66/1.27
% 1.66/1.27
% 1.66/1.27 %
% 1.66/1.27
% 1.66/1.27 % ------ Proving...
% 1.66/1.27 %
% 1.66/1.27
% 1.66/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.27
% 1.66/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/1.27
% 1.66/1.27
%------------------------------------------------------------------------------