%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 03:32:54 PM UTC 2026
% Result : Unsatisfiable 2.33s 1.28s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 40 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 13 ~; 3 |; 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : aux(X0,X1,X2,btrue) = union(X2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
fof(f3,axiom,
! [X0] : barbar(btrue,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(f4,plain,
! [X0] : btrue = barbar(btrue,X0),
inference(reorient_equations,[],[f3]) ).
fof(f11,axiom,
eqNat(z,z) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(f12,plain,
btrue = eqNat(z,z),
inference(reorient_equations,[],[f11]) ).
fof(f15,axiom,
! [X2,X0,X1] : elem(X0,cons(X1,X2)) = barbar(eqNat(X0,X1),elem(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(f16,axiom,
! [X0] : union(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f17,axiom,
! [X2,X0,X1] : union(cons(X0,X1),X2) = aux(X2,X0,X1,elem(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f18,axiom,
! [X0,X1] : prop_union_comm(X0,X1) = eq(union(X0,X1),union(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f30,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(f31,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f30]) ).
fof(f32,axiom,
! [X0] : eq3(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(f33,plain,
! [X0] : btrue = eq3(X0,X0),
inference(reorient_equations,[],[f32]) ).
fof(f36,axiom,
! [X2,X3,X0,X1] :
( eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3)
| eq2(X0,X1) != btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3)
| btrue != eq2(X0,X1) ),
inference(reorient_equations,[],[f36]) ).
fof(f40,axiom,
! [X0,X1] : eq(cons(X0,X1),nil) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(f41,plain,
! [X0,X1] : bfalse = eq(cons(X0,X1),nil),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
! [X0,X1] : eq3(prop_union_comm(X0,X1),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f43,plain,
! [X0,X1] : btrue != eq3(prop_union_comm(X0,X1),bfalse),
inference(reorient_equations,[],[f42]) ).
fof(f44,plain,
! [X0,X1] : btrue != eq3(eq(union(X0,X1),union(X1,X0)),bfalse),
inference(definition_unfolding,[],[f43,f18]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : aux(X0,X1,X2,btrue) = union(X2,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_77,plain,
! [X0: $i] : barbar(btrue,X0) = btrue,
inference(cnf_transformation,[],[f4]) ).
tcf(c_82,plain,
eqNat(z,z) = btrue,
inference(cnf_transformation,[],[f12]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] : barbar(eqNat(X0,X1),elem(X0,X2)) = elem(X0,cons(X1,X2)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_85,plain,
! [X0: $i] : union(nil,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] : aux(X0,X1,X2,elem(X1,X0)) = union(cons(X1,X2),X0),
inference(cnf_transformation,[],[f17]) ).
tcf(c_93,plain,
! [X0: $i] : eq2(X0,X0) = btrue,
inference(cnf_transformation,[],[f31]) ).
tcf(c_94,plain,
! [X0: $i] : eq3(X0,X0) = btrue,
inference(cnf_transformation,[],[f33]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3) )
| ( eq2(X0,X1) != btrue ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] : eq(cons(X0,X1),nil) = bfalse,
inference(cnf_transformation,[],[f41]) ).
tcf(c_99,negated_conjecture,
! [X0: $i,X1: $i] : eq3(eq(union(X0,X1),union(X1,X0)),bfalse) != btrue,
inference(cnf_transformation,[],[f44]) ).
tcf(c_193,negated_conjecture,
! [X0: $i,X1: $i] : eq3(eq(union(X0,X1),union(X1,X0)),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_337,plain,
! [X0: $i] : barbar(btrue,elem(z,X0)) = elem(z,cons(z,X0)),
inference(superposition,[status(thm)],[c_82,c_84]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i,X2: $i] : eq(cons(X0,X1),cons(X0,X2)) = eq(X1,X2),
inference(superposition,[status(thm)],[c_93,c_96]) ).
tcf(c_374,plain,
! [X0: $i] : elem(z,cons(z,X0)) = btrue,
inference(demodulation,[status(thm)],[c_337,c_77]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] : aux(cons(z,X0),z,X1,btrue) = union(cons(z,X1),cons(z,X0)),
inference(superposition,[status(thm)],[c_374,c_86]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i] : union(cons(z,X0),cons(z,X1)) = union(X0,cons(z,X1)),
inference(demodulation,[status(thm)],[c_376,c_75]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] : eq3(eq(union(cons(z,X0),cons(z,X1)),union(X1,cons(z,X0))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_422,c_193]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i] : eq3(eq(union(X0,cons(z,X1)),union(X1,cons(z,X0))),bfalse) != btrue,
inference(light_normalisation,[status(thm)],[c_424,c_422]) ).
tcf(c_478,plain,
! [X0: $i] : eq3(eq(cons(z,X0),union(X0,cons(z,nil))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_85,c_425]) ).
tcf(c_501,plain,
! [X0: $i] : eq3(eq(cons(z,cons(z,X0)),union(X0,cons(z,nil))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_422,c_478]) ).
tcf(c_520,plain,
eq3(eq(cons(z,cons(z,nil)),cons(z,nil)),bfalse) != btrue,
inference(superposition,[status(thm)],[c_85,c_501]) ).
tcf(c_522,plain,
$false,
inference(ground_joinability,[status(thm)],[c_520,c_94,c_98,c_369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 23:47:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.33/1.28 % SZS status Started for theBenchmark.p
% 2.33/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.33/1.28
% 2.33/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/1.28
% 2.33/1.28 % ------ iProver source info
% 2.33/1.28
% 2.33/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/1.28 % git: non_committed_changes: false
% 2.33/1.28
% 2.33/1.28 % ------ Parsing...% successful
% 2.33/1.28
% 2.33/1.28
% 2.33/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/1.28
% 2.33/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.33/1.28
% 2.33/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.33/1.28
% 2.33/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.33/1.28 % ------ Proving...
% 2.33/1.28 % ------ Problem Properties
% 2.33/1.28
% 2.33/1.28 %
% 2.33/1.28 % clauses 25
% 2.33/1.28 % conjectures 1
% 2.33/1.28 % EPR 0
% 2.33/1.28 % Horn 25
% 2.33/1.28 % unary 23
% 2.33/1.28 % binary 2
% 2.33/1.28 % lits 27
% 2.33/1.28 % lits eq 27
% 2.33/1.28 % fd_pure 0
% 2.33/1.28 % fd_pseudo 0
% 2.33/1.28 % fd_cond 0
% 2.33/1.28 % fd_pseudo_cond 0
% 2.33/1.28 % AC symbols 0
% 2.33/1.28
% 2.33/1.28 % ------ Schedule dynamic 5 is on
% 2.33/1.28
% 2.33/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.33/1.28
% 2.33/1.28
% 2.33/1.28 % ------
% 2.33/1.28 % Current options:
% 2.33/1.28 % ------
% 2.33/1.28
% 2.33/1.28
% 2.33/1.28 %
% 2.33/1.28
% 2.33/1.28 % ------ Proving...
% 2.33/1.28 %
% 2.33/1.28
% 2.33/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.33/1.28
% 2.33/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/1.29
% 2.33/1.29
%------------------------------------------------------------------------------