%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET121-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 02:46:41 PM UTC 2026
% Result : Unsatisfiable 8.31s 1.73s
% Output : CNFRefutation 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 23 unt; 0 def)
% Number of atoms : 61 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 36 ( 17 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f104,axiom,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f124,axiom,
! [X0,X1] :
( unordered_pair(X0,X1) = singleton(X1)
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f138,axiom,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f175,axiom,
! [X0] :
( first(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f177,axiom,
! [X0] :
( first(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f191,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_OP_determines_components2_1) ).
fof(f192,negated_conjecture,
first(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_OP_determines_components2_2) ).
fof(f193,plain,
ordered_pair(x,y) != first(ordered_pair(x,y)),
inference(reorient_equations,[],[f192]) ).
fof(f194,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f195,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) != first(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),
inference(definition_unfolding,[],[f193,f194,f194]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f104,f194]) ).
fof(f213,plain,
! [X0] :
( first(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f177,f194]) ).
fof(f215,plain,
! [X0] :
( first(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f175,f194]) ).
fof(f222,plain,
! [X0] :
( unordered_pair(X0,X0) = null_class
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f243,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X1)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f124,f12]) ).
tcf(c_218,negated_conjecture,
~ member(y,universal_class),
inference(cnf_transformation,[],[f191]) ).
tcf(c_219,negated_conjecture,
first(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(cnf_transformation,[],[f195]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_237,plain,
! [X0: $i] :
( ( first(X0) = X0 )
| ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_239,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| ( first(X0) = X0 ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_246,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( unordered_pair(X0,X0) = null_class ) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( unordered_pair(X0,X0) = unordered_pair(X1,X0) ) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_2155,plain,
unordered_pair(y,y) = null_class,
inference(superposition,[status(thm)],[c_246,c_218]) ).
tcf(c_2156,plain,
first(unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),
inference(demodulation,[status(thm)],[c_219,c_2155]) ).
tcf(c_2163,plain,
first(unordered_pair(unordered_pair(null_class,x),unordered_pair(x,x))) != unordered_pair(unordered_pair(null_class,x),unordered_pair(x,x)),
inference(demodulation,[status(thm)],[c_2156,c_285]) ).
tcf(c_2327,plain,
! [X0: $i] : unordered_pair(X0,X0) = unordered_pair(y,X0),
inference(superposition,[status(thm)],[c_283,c_218]) ).
tcf(c_2330,plain,
first(unordered_pair(unordered_pair(null_class,x),unordered_pair(y,x))) != unordered_pair(unordered_pair(null_class,x),unordered_pair(y,x)),
inference(demodulation,[status(thm)],[c_2163,c_2327]) ).
tcf(c_2362,plain,
! [X0: $i] : unordered_pair(X0,X0) = unordered_pair(X0,y),
inference(superposition,[status(thm)],[c_2327,c_285]) ).
tcf(c_3101,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(y,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,null_class)),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_2155,c_224]) ).
tcf(c_3102,plain,
! [X0: $i,X1: $i,X2: $i] : ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,null_class)),cross_product(X1,X2)),
inference(forward_subsumption_resolution,[status(thm)],[c_3101,c_218]) ).
tcf(c_3414,plain,
! [X0: $i,X1: $i,X2: $i] : ~ member(unordered_pair(unordered_pair(X0,null_class),unordered_pair(X0,X0)),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_285,c_3102]) ).
tcf(c_3461,plain,
! [X0: $i,X1: $i,X2: $i] : ~ member(unordered_pair(unordered_pair(X0,null_class),unordered_pair(y,X0)),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_2327,c_3414]) ).
tcf(c_3890,plain,
! [X0: $i,X1: $i,X2: $i] : ~ member(unordered_pair(unordered_pair(null_class,X0),unordered_pair(y,X0)),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_285,c_3461]) ).
tcf(c_4908,plain,
! [X0: $i] :
( ( first(X0) = X0 )
| ( unordered_pair(unordered_pair(y,first(X0)),unordered_pair(first(X0),unordered_pair(y,second(X0)))) = X0 ) ),
inference(demodulation,[status(thm)],[c_237,c_285,c_2362]) ).
tcf(c_6246,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(y,first(X0)),unordered_pair(first(X0),unordered_pair(y,second(X0)))),cross_product(universal_class,universal_class))
| ( first(X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_239,c_285,c_2362]) ).
tcf(c_6253,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ( first(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_4908,c_6246]) ).
tcf(c_12069,plain,
! [X0: $i] : first(unordered_pair(unordered_pair(null_class,X0),unordered_pair(y,X0))) = unordered_pair(unordered_pair(null_class,X0),unordered_pair(y,X0)),
inference(superposition,[status(thm)],[c_6253,c_3890]) ).
tcf(c_12091,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2330,c_12069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET121-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:57:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 8.31/1.73 % SZS status Started for theBenchmark.p
% 8.31/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.31/1.73
% 8.31/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.31/1.73
% 8.31/1.73 % ------ iProver source info
% 8.31/1.73
% 8.31/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 8.31/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.31/1.73 % git: non_committed_changes: false
% 8.31/1.73
% 8.31/1.73 % ------ Parsing...% successful
% 8.31/1.73
% 8.31/1.73
% 8.31/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.31/1.73
% 8.31/1.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 8.31/1.73
% 8.31/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.31/1.73
% 8.31/1.73 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.31/1.73 % ------ Proving...
% 8.31/1.73 % ------ Problem Properties
% 8.31/1.73
% 8.31/1.73 %
% 8.31/1.73 % clauses 62
% 8.31/1.73 % conjectures 2
% 8.31/1.73 % EPR 10
% 8.31/1.73 % Horn 46
% 8.31/1.73 % unary 15
% 8.31/1.73 % binary 30
% 8.31/1.73 % lits 127
% 8.31/1.73 % lits eq 46
% 8.31/1.73 % fd_pure 0
% 8.31/1.73 % fd_pseudo 0
% 8.31/1.73 % fd_cond 1
% 8.31/1.73 % fd_pseudo_cond 11
% 8.31/1.73 % AC symbols 0
% 8.31/1.73
% 8.31/1.73 % ------ Schedule dynamic 5 is on
% 8.31/1.73
% 8.31/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.31/1.73
% 8.31/1.73
% 8.31/1.73 % ------
% 8.31/1.73 % Current options:
% 8.31/1.73 % ------
% 8.31/1.73
% 8.31/1.73
% 8.31/1.73 %
% 8.31/1.73
% 8.31/1.73 % ------ Proving...
% 8.31/1.73 %
% 8.31/1.73
% 8.31/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.31/1.73
% 8.31/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.31/1.73
% 8.31/1.73
%------------------------------------------------------------------------------