%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:47:35 PM UTC 2026
% Result : Theorem 0.75s 1.18s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 37 !; 3 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1,X2] : difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_difference_union) ).
fof(f3,axiom,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(f12,conjecture,
! [X0,X1,X2] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th97) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] : difference(symmetric_difference(X0,X1),X2) != union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
difference(symmetric_difference(sK0,sK1),sK2) != union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
fof(f29,plain,
difference(symmetric_difference(sK0,sK1),sK2) != union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))),
inference(cnf_transformation,[],[f16]) ).
fof(f32,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X2,X0,X1] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f52,plain,
union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))) != difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2),
inference(definition_unfolding,[],[f29,f32]) ).
tcf(c_49,negated_conjecture,
union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))) != difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2),
inference(cnf_transformation,[],[f52]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : union(difference(X0,X1),difference(X2,X1)) = difference(union(X0,X2),X1),
inference(cnf_transformation,[],[f36]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : union(difference(X0,union(X1,X2)),difference(X3,X2)) = difference(union(difference(X0,X1),X3),X2),
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_2332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : union(difference(X0,union(X1,X2)),difference(X3,union(X4,X2))) = difference(union(difference(X0,X1),difference(X3,X4)),X2),
inference(superposition,[status(thm)],[c_56,c_646]) ).
tcf(c_2416,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_2332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n008.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:29:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 0.75/1.18 % SZS status Started for theBenchmark.p
% 0.75/1.18 % SZS status Theorem for theBenchmark.p
% 0.75/1.18
% 0.75/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.75/1.18
% 0.75/1.18 % ------ iProver source info
% 0.75/1.18
% 0.75/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.75/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.75/1.18 % git: non_committed_changes: false
% 0.75/1.18
% 0.75/1.18 % ------ Parsing...
% 0.75/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.75/1.18
% 0.75/1.18 % ------ 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 %
% 0.75/1.18
% 0.75/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.75/1.18
% 0.75/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.75/1.18 % ------ Proving...
% 0.75/1.18 % ------ Problem Properties
% 0.75/1.18
% 0.75/1.18 %
% 0.75/1.18 % clauses 17
% 0.75/1.18 % conjectures 1
% 0.75/1.18 % EPR 3
% 0.75/1.18 % Horn 13
% 0.75/1.18 % unary 5
% 0.75/1.18 % binary 6
% 0.75/1.18 % lits 35
% 0.75/1.18 % lits eq 7
% 0.75/1.18 % fd_pure 0
% 0.75/1.18 % fd_pseudo 0
% 0.75/1.18 % fd_cond 0
% 0.75/1.18 % fd_pseudo_cond 3
% 0.75/1.18 % AC symbols 0
% 0.75/1.18
% 0.75/1.18 % ------ Schedule dynamic 5 is on
% 0.75/1.18
% 0.75/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.75/1.18
% 0.75/1.18
% 0.75/1.18 % ------
% 0.75/1.18 % Current options:
% 0.75/1.18 % ------
% 0.75/1.18
% 0.75/1.18
% 0.75/1.18 %
% 0.75/1.18
% 0.75/1.18 % ------ Proving...
% 0.75/1.18 %
% 0.75/1.18
% 0.75/1.18 % SZS status Theorem for theBenchmark.p
% 0.75/1.18
% 0.75/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.75/1.18
% 0.75/1.18
%------------------------------------------------------------------------------