%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET994+1 : 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 : n006.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 02:49:17 PM UTC 2026
% Result : Theorem 3.88s 1.32s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 88 ( 36 unt; 0 def)
% Number of atoms : 228 ( 82 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 241 ( 101 ~; 95 |; 31 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 94 !; 7 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f8,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f9,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f10,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f20,axiom,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = n0 )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(f21,axiom,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = n1 )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(f22,axiom,
empty(n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc0_boole) ).
fof(f23,axiom,
~ empty(n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc1_boole) ).
fof(f24,conjecture,
! [X0] :
( ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_dom(X2) = X0
& relation_dom(X1) = X0 )
=> X1 = X2 ) ) )
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_dom(X2) = X0
& relation_dom(X1) = X0 )
=> X1 = X2 ) ) )
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f31,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = n0 )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = n1 )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f47,plain,
? [X0] :
( ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != X0
| relation_dom(X1) != X0
| X1 = X2 ) )
& empty_set != X0 ),
inference(ennf_transformation,[],[f25]) ).
fof(f48,plain,
? [X0] :
( ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != X0
| relation_dom(X1) != X0
| X1 = X2 ) )
& empty_set != X0 ),
inference(flattening,[],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f31]) ).
fof(f59,plain,
! [X0] : element(sK0(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f4]) ).
fof(f68,plain,
! [X0] :
( ! [X2] :
( ~ in(X2,X0)
| n0 = apply(sK9(X0),X2) )
& relation_dom(sK9(X0)) = X0
& function(sK9(X0))
& relation(sK9(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f45]) ).
fof(f69,plain,
! [X0] :
( ! [X2] :
( ~ in(X2,X0)
| n1 = apply(sK10(X0),X2) )
& relation_dom(sK10(X0)) = X0
& function(sK10(X0))
& relation(sK10(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f46]) ).
fof(f70,plain,
( ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != sK11
| relation_dom(X1) != sK11
| X1 = X2 ) )
& empty_set != sK11 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f48]) ).
fof(f74,plain,
! [X0] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f59]) ).
fof(f80,plain,
empty(empty_set),
inference(cnf_transformation,[],[f8]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f83,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f98,plain,
! [X2,X0] :
( ~ in(X2,X0)
| n0 = apply(sK9(X0),X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f99,plain,
! [X0] : relation_dom(sK9(X0)) = X0,
inference(cnf_transformation,[],[f68]) ).
fof(f100,plain,
! [X0] : function(sK9(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f101,plain,
! [X0] : relation(sK9(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f102,plain,
! [X2,X0] :
( ~ in(X2,X0)
| n1 = apply(sK10(X0),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f103,plain,
! [X0] : relation_dom(sK10(X0)) = X0,
inference(cnf_transformation,[],[f69]) ).
fof(f104,plain,
! [X0] : function(sK10(X0)),
inference(cnf_transformation,[],[f69]) ).
fof(f105,plain,
! [X0] : relation(sK10(X0)),
inference(cnf_transformation,[],[f69]) ).
fof(f106,plain,
empty(n0),
inference(cnf_transformation,[],[f22]) ).
fof(f107,plain,
~ empty(n1),
inference(cnf_transformation,[],[f23]) ).
fof(f108,plain,
! [X2,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != sK11
| relation_dom(X1) != sK11
| X1 = X2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f109,plain,
empty_set != sK11,
inference(cnf_transformation,[],[f70]) ).
fof(f111,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f115,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_52,plain,
! [X0: $i] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f74]) ).
tcf(c_57,plain,
empty(empty_set),
inference(cnf_transformation,[],[f80]) ).
tcf(c_59,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_60,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_76,plain,
! [X0: $i] : relation(sK9(X0)),
inference(cnf_transformation,[],[f101]) ).
tcf(c_77,plain,
! [X0: $i] : function(sK9(X0)),
inference(cnf_transformation,[],[f100]) ).
tcf(c_78,plain,
! [X0: $i] : relation_dom(sK9(X0)) = X0,
inference(cnf_transformation,[],[f99]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ( apply(sK9(X1),X0) = n0 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_80,plain,
! [X0: $i] : relation(sK10(X0)),
inference(cnf_transformation,[],[f105]) ).
tcf(c_81,plain,
! [X0: $i] : function(sK10(X0)),
inference(cnf_transformation,[],[f104]) ).
tcf(c_82,plain,
! [X0: $i] : relation_dom(sK10(X0)) = X0,
inference(cnf_transformation,[],[f103]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ( apply(sK10(X1),X0) = n1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_84,plain,
empty(n0),
inference(cnf_transformation,[],[f106]) ).
tcf(c_85,plain,
~ empty(n1),
inference(cnf_transformation,[],[f107]) ).
tcf(c_86,negated_conjecture,
empty_set != sK11,
inference(cnf_transformation,[],[f109]) ).
tcf(c_87,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ( relation_dom(X1) != sK11 )
| ( relation_dom(X0) != sK11 ) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_93,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_613,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ( relation_dom(X1) != sK11 )
| ( relation_dom(X0) != sK11 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_614,negated_conjecture,
empty_set != sK11,
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_1090,plain,
! [X0: $i,X1: $i] :
( ( sK10(X1) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK10(X1))
| ~ function(sK10(X1))
| ( X1 != sK11 )
| ( relation_dom(X0) != sK11 ) ),
inference(superposition,[status(thm)],[c_82,c_613]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i] :
( ( sK10(X1) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ( X1 != sK11 )
| ( relation_dom(X0) != sK11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1090,c_80,c_81]) ).
tcf(c_1121,plain,
! [X0: $i,X1: $i] :
( ( sK9(X0) = sK10(X1) )
| ~ relation(sK9(X0))
| ~ function(sK9(X0))
| ( X1 != sK11 )
| ( X0 != sK11 ) ),
inference(superposition,[status(thm)],[c_78,c_1095]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i] :
( ( sK9(X0) = sK10(X1) )
| ( X1 != sK11 )
| ( X0 != sK11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1121,c_76,c_77]) ).
tcf(c_1146,plain,
! [X0: $i] :
( ( sK10(X0) = sK9(sK11) )
| ( X0 != sK11 ) ),
inference(equality_resolution,[status(thm)],[c_1127]) ).
tcf(c_1158,plain,
sK9(sK11) = sK10(sK11),
inference(equality_resolution,[status(thm)],[c_1146]) ).
tcf(c_1255,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_60,c_93]) ).
tcf(c_1259,plain,
empty_set = n0,
inference(superposition,[status(thm)],[c_84,c_93]) ).
tcf(c_1272,plain,
! [X0: $i,X1: $i] :
( ( apply(sK9(X1),X0) = empty_set )
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_79,c_1259]) ).
tcf(c_1318,plain,
! [X0: $i] :
( empty(sK10(X0))
| ~ empty(X0)
| ~ relation(sK10(X0)) ),
inference(superposition,[status(thm)],[c_82,c_59]) ).
tcf(c_1320,plain,
! [X0: $i] :
( empty(sK10(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1318,c_80]) ).
tcf(c_1332,plain,
( empty(sK9(sK11))
| ~ empty(sK11) ),
inference(superposition,[status(thm)],[c_1158,c_1320]) ).
tcf(c_1356,plain,
! [X0: $i] :
( empty(X0)
| in(sK0(X0),X0) ),
inference(superposition,[status(thm)],[c_52,c_89]) ).
tcf(c_1423,plain,
( ( relation_dom(sK9(sK11)) = empty_set )
| ~ empty(sK11) ),
inference(superposition,[status(thm)],[c_1332,c_1255]) ).
tcf(c_1445,plain,
( ( empty_set = sK11 )
| ~ empty(sK11) ),
inference(demodulation,[status(thm)],[c_1423,c_78]) ).
tcf(c_1446,plain,
~ empty(sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_1445,c_614]) ).
tcf(c_1470,plain,
! [X0: $i] :
( empty(X0)
| ( apply(sK10(X0),sK0(X0)) = n1 ) ),
inference(superposition,[status(thm)],[c_1356,c_83]) ).
tcf(c_1471,plain,
! [X0: $i] :
( empty(X0)
| ( apply(sK9(X0),sK0(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_1356,c_1272]) ).
tcf(c_1718,plain,
apply(sK10(sK11),sK0(sK11)) = n1,
inference(superposition,[status(thm)],[c_1470,c_1446]) ).
tcf(c_1719,plain,
apply(sK9(sK11),sK0(sK11)) = n1,
inference(light_normalisation,[status(thm)],[c_1718,c_1158]) ).
tcf(c_2169,plain,
apply(sK9(sK11),sK0(sK11)) = empty_set,
inference(superposition,[status(thm)],[c_1471,c_1446]) ).
tcf(c_2227,plain,
empty_set = n1,
inference(demodulation,[status(thm)],[c_1719,c_2169]) ).
tcf(c_2236,plain,
~ empty(empty_set),
inference(demodulation,[status(thm)],[c_85,c_2227]) ).
tcf(c_2237,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2236,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 % Computer : n006.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Thu Sep 24 12:31:29 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 0.14/0.46
% 0.14/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.46
% 0.14/0.46 % Detected problem language: tptp
% 0.19/0.47 % Proving...
% 3.88/1.32 % SZS status Started for theBenchmark.p
% 3.88/1.32 % SZS status Theorem for theBenchmark.p
% 3.88/1.32
% 3.88/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.88/1.32
% 3.88/1.32 % ------ iProver source info
% 3.88/1.32
% 3.88/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 3.88/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.88/1.32 % git: non_committed_changes: false
% 3.88/1.32
% 3.88/1.32 % ------ Parsing...
% 3.88/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.88/1.32
% 3.88/1.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.88/1.32
% 3.88/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.88/1.32
% 3.88/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.88/1.32 % ------ Proving...
% 3.88/1.32 % ------ Problem Properties
% 3.88/1.32
% 3.88/1.32 %
% 3.88/1.32 % clauses 43
% 3.88/1.32 % conjectures 2
% 3.88/1.32 % EPR 22
% 3.88/1.32 % Horn 41
% 3.88/1.32 % unary 25
% 3.88/1.32 % binary 12
% 3.88/1.32 % lits 71
% 3.88/1.32 % lits eq 10
% 3.88/1.32 % fd_pure 0
% 3.88/1.32 % fd_pseudo 0
% 3.88/1.32 % fd_cond 1
% 3.88/1.32 % fd_pseudo_cond 2
% 3.88/1.32 % AC symbols 0
% 3.88/1.32
% 3.88/1.32 % ------ Schedule dynamic 5 is on
% 3.88/1.32
% 3.88/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.88/1.32
% 3.88/1.32
% 3.88/1.32 % ------
% 3.88/1.32 % Current options:
% 3.88/1.32 % ------
% 3.88/1.32
% 3.88/1.32
% 3.88/1.32 %
% 3.88/1.32
% 3.88/1.32 % ------ Proving...
% 3.88/1.32 %
% 3.88/1.32
% 3.88/1.32 % SZS status Theorem for theBenchmark.p
% 3.88/1.32
% 3.88/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.88/1.33
% 3.88/1.33
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