%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 03:29:11 PM UTC 2026
% Result : Theorem 3.66s 6.40s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 44 unt; 0 def)
% Number of atoms : 164 ( 85 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 138 ( 57 ~; 51 |; 25 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 48 !; 3 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( bool(X0)
<=> ( X0 = true
| X0 = false ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_bool) ).
fof(f3,axiom,
( d(err)
& d(false)
& d(true) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).
fof(f4,axiom,
! [X0,X1] :
( forallprefers(X0,X1)
<=> ( ( X1 = true
& X0 = false )
| ( bool(X1)
& ~ bool(X0)
& d(X1)
& d(X0) )
| ( d(X1)
& ~ d(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).
fof(f6,axiom,
! [X0] :
( ( phi(X0) = err
& ~ d(X0) )
| ( phi(X0) = X0
& d(X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_phi) ).
fof(f7,axiom,
! [X0] :
( prop(X0) = true
<=> bool(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',prop_true) ).
fof(f8,axiom,
! [X0] :
( prop(X0) = false
<=> ~ bool(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',prop_false) ).
fof(f14,axiom,
! [X0] : lazy_impl(false,X0) = true,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).
fof(f15,axiom,
! [X0] : lazy_impl(true,X0) = phi(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).
fof(f38,axiom,
false1 = false,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_false1) ).
fof(f39,axiom,
! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_f7) ).
fof(f40,axiom,
? [X0] :
( ~ ? [X1] : forallprefers(f7(X1),f7(X0))
& false2 = phi(f7(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_false2) ).
fof(f45,conjecture,
false1 = false2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false1_false2) ).
fof(f46,negated_conjecture,
false1 != false2,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
false1 != false2,
inference(flattening,[],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ( ( X1 = true
& X0 = false )
| ( bool(X1)
& ~ bool(X0)
& d(X1)
& d(X0) )
| ( d(X1)
& ~ d(X0) ) )
=> forallprefers(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f50,plain,
! [X0,X1] :
( ( ( true != X1
| false != X0 )
& ( ~ bool(X1)
| bool(X0)
| ~ d(X1)
| ~ d(X0) )
& ( ~ d(X1)
| d(X0) ) )
| forallprefers(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f75,plain,
? [X0] :
( ! [X1] : ~ forallprefers(f7(X1),f7(X0))
& false2 = phi(f7(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f77,plain,
! [X0] :
( ( ~ bool(X0)
| X0 = true
| X0 = false )
& ( ( true != X0
& false != X0 )
| bool(X0) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f78,plain,
! [X0] :
( ( ~ bool(X0)
| X0 = true
| X0 = false )
& ( ( true != X0
& false != X0 )
| bool(X0) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( true != prop(X0)
| bool(X0) )
& ( ~ bool(X0)
| prop(X0) = true ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f80,plain,
! [X0] :
( ( false != prop(X0)
| ~ bool(X0) )
& ( bool(X0)
| prop(X0) = false ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f87,plain,
( ! [X1] : ~ forallprefers(f7(X1),f7(sK6))
& false2 = phi(f7(sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f75]) ).
fof(f88,plain,
! [X0] :
( ~ bool(X0)
| true = X0
| false = X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f90,plain,
! [X0] :
( false != X0
| bool(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f95,plain,
d(false),
inference(cnf_transformation,[],[f3]) ).
fof(f96,plain,
d(true),
inference(cnf_transformation,[],[f3]) ).
fof(f97,plain,
! [X0,X1] :
( true != X1
| false != X0
| forallprefers(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f104,plain,
! [X0] :
( ~ d(X0)
| phi(X0) = X0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f107,plain,
! [X0] :
( true != prop(X0)
| bool(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f108,plain,
! [X0] :
( ~ bool(X0)
| true = prop(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f110,plain,
! [X0] :
( bool(X0)
| false = prop(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0] : true = lazy_impl(false,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f117,plain,
! [X0] : phi(X0) = lazy_impl(true,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f146,plain,
false = false1,
inference(cnf_transformation,[],[f38]) ).
fof(f147,plain,
! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
inference(cnf_transformation,[],[f39]) ).
fof(f148,plain,
! [X1] : ~ forallprefers(f7(X1),f7(sK6)),
inference(cnf_transformation,[],[f87]) ).
fof(f149,plain,
false2 = phi(f7(sK6)),
inference(cnf_transformation,[],[f87]) ).
fof(f154,plain,
false1 != false2,
inference(cnf_transformation,[],[f47]) ).
fof(f162,plain,
! [X0] :
( false1 != X0
| bool(X0) ),
inference(definition_unfolding,[],[f90,f146]) ).
fof(f163,plain,
! [X0] :
( ~ bool(X0)
| true = X0
| false1 = X0 ),
inference(definition_unfolding,[],[f88,f146]) ).
fof(f166,plain,
d(false1),
inference(definition_unfolding,[],[f95,f146]) ).
fof(f167,plain,
! [X0,X1] :
( true != X1
| false1 != X0
| forallprefers(X0,X1) ),
inference(definition_unfolding,[],[f97,f146]) ).
fof(f170,plain,
! [X0] :
( ~ d(X0)
| lazy_impl(true,X0) = X0 ),
inference(definition_unfolding,[],[f104,f117]) ).
fof(f172,plain,
! [X0] :
( bool(X0)
| prop(X0) = false1 ),
inference(definition_unfolding,[],[f110,f146]) ).
fof(f178,plain,
! [X0] : true = lazy_impl(false1,X0),
inference(definition_unfolding,[],[f116,f146]) ).
fof(f193,plain,
false2 = lazy_impl(true,lazy_impl(prop(sK6),sK6)),
inference(definition_unfolding,[],[f149,f117,f147]) ).
fof(f194,plain,
! [X1] : ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(sK6),sK6)),
inference(definition_unfolding,[],[f148,f147,f147]) ).
fof(f198,plain,
bool(false1),
inference(equality_resolution,[],[f162]) ).
fof(f200,plain,
! [X1] :
( true != X1
| forallprefers(false1,X1) ),
inference(equality_resolution,[],[f167]) ).
fof(f201,plain,
forallprefers(false1,true),
inference(equality_resolution,[],[f200]) ).
tcf(c_49,plain,
bool(false1),
inference(cnf_transformation,[],[f198]) ).
tcf(c_51,plain,
! [X0: $i] :
( ( X0 = true )
| ( X0 = false1 )
| ~ bool(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_55,plain,
d(true),
inference(cnf_transformation,[],[f96]) ).
tcf(c_56,plain,
d(false1),
inference(cnf_transformation,[],[f166]) ).
tcf(c_60,plain,
forallprefers(false1,true),
inference(cnf_transformation,[],[f201]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( lazy_impl(true,X0) = X0 )
| ~ d(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_67,plain,
! [X0: $i] :
( ( prop(X0) = true )
| ~ bool(X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_68,plain,
! [X0: $i] :
( bool(X0)
| ( prop(X0) != true ) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_69,plain,
! [X0: $i] :
( bool(X0)
| ( prop(X0) = false1 ) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_76,plain,
! [X0: $i] : lazy_impl(false1,X0) = true,
inference(cnf_transformation,[],[f178]) ).
tcf(c_94,plain,
lazy_impl(true,lazy_impl(prop(sK6),sK6)) = false2,
inference(cnf_transformation,[],[f193]) ).
tcf(c_95,plain,
! [X0: $i] : ~ forallprefers(lazy_impl(prop(X0),X0),lazy_impl(prop(sK6),sK6)),
inference(cnf_transformation,[],[f194]) ).
tcf(c_99,negated_conjecture,
false1 != false2,
inference(cnf_transformation,[],[f154]) ).
tcf(c_822,negated_conjecture,
false1 != false2,
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_1729,plain,
prop(false1) = true,
inference(superposition,[status(thm)],[c_49,c_67]) ).
tcf(c_1731,plain,
! [X0: $i] :
( ( prop(X0) = true )
| ( prop(X0) = false1 ) ),
inference(superposition,[status(thm)],[c_69,c_67]) ).
tcf(c_1744,plain,
lazy_impl(true,true) = true,
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_1745,plain,
lazy_impl(true,false1) = false1,
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_1988,plain,
~ forallprefers(lazy_impl(true,false1),lazy_impl(prop(sK6),sK6)),
inference(superposition,[status(thm)],[c_1729,c_95]) ).
tcf(c_1990,plain,
~ forallprefers(false1,lazy_impl(prop(sK6),sK6)),
inference(light_normalisation,[status(thm)],[c_1988,c_1745]) ).
tcf(c_2003,plain,
( ( prop(sK6) = true )
| ~ forallprefers(false1,lazy_impl(false1,sK6)) ),
inference(superposition,[status(thm)],[c_1731,c_1990]) ).
tcf(c_3412,plain,
( ( prop(sK6) = true )
| ~ forallprefers(false1,true) ),
inference(demodulation,[status(thm)],[c_2003,c_76]) ).
tcf(c_3413,plain,
prop(sK6) = true,
inference(forward_subsumption_resolution,[status(thm)],[c_3412,c_60]) ).
tcf(c_3416,plain,
~ forallprefers(false1,lazy_impl(true,sK6)),
inference(demodulation,[status(thm)],[c_1990,c_3413]) ).
tcf(c_3418,plain,
lazy_impl(true,lazy_impl(true,sK6)) = false2,
inference(demodulation,[status(thm)],[c_94,c_3413]) ).
tcf(c_3431,plain,
bool(sK6),
inference(superposition,[status(thm)],[c_3413,c_68]) ).
tcf(c_3441,plain,
( ( true = sK6 )
| ( false1 = sK6 ) ),
inference(superposition,[status(thm)],[c_3431,c_51]) ).
tcf(c_3550,plain,
( ( true = sK6 )
| ( lazy_impl(true,lazy_impl(true,false1)) = false2 ) ),
inference(superposition,[status(thm)],[c_3441,c_3418]) ).
tcf(c_3567,plain,
( ( true = sK6 )
| ( false1 = false2 ) ),
inference(light_normalisation,[status(thm)],[c_3550,c_1745]) ).
tcf(c_3568,plain,
true = sK6,
inference(forward_subsumption_resolution,[status(thm)],[c_3567,c_822]) ).
tcf(c_3577,plain,
~ forallprefers(false1,lazy_impl(true,true)),
inference(demodulation,[status(thm)],[c_3416,c_3568]) ).
tcf(c_3582,plain,
~ forallprefers(false1,true),
inference(light_normalisation,[status(thm)],[c_3577,c_1744]) ).
tcf(c_3583,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3582,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 % Computer : n007.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Thu Sep 24 21:37:13 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.48 Running first-order theorem proving
% 0.16/5.48 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
% 0.20/5.50
% 0.20/5.50 % ======== iProver multi-core TPTP/SMT =========
% 0.20/5.50
% 0.20/5.50 % Detected problem language: tptp
% 0.20/5.51 % Proving...
% 3.66/6.40 % SZS status Started for theBenchmark.p
% 3.66/6.40 % SZS status Theorem for theBenchmark.p
% 3.66/6.40
% 3.66/6.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.66/6.40
% 3.66/6.40 % ------ iProver source info
% 3.66/6.40
% 3.66/6.40 % git: date: 2026-07-19 20:42:38 +0200
% 3.66/6.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.66/6.40 % git: non_committed_changes: false
% 3.66/6.40
% 3.66/6.40 % ------ Parsing...
% 3.66/6.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.66/6.40
% 3.66/6.40 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.66/6.40
% 3.66/6.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.66/6.40
% 3.66/6.40 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.66/6.40 % ------ Proving...
% 3.66/6.40 % ------ Problem Properties
% 3.66/6.40
% 3.66/6.40 %
% 3.66/6.40 % clauses 51
% 3.66/6.40 % conjectures 1
% 3.66/6.40 % EPR 16
% 3.66/6.40 % Horn 34
% 3.66/6.40 % unary 24
% 3.66/6.40 % binary 19
% 3.66/6.40 % lits 88
% 3.66/6.40 % lits eq 35
% 3.66/6.40 % fd_pure 0
% 3.66/6.40 % fd_pseudo 0
% 3.66/6.40 % fd_cond 1
% 3.66/6.40 % fd_pseudo_cond 0
% 3.66/6.40 % AC symbols 0
% 3.66/6.40
% 3.66/6.40 % ------ Schedule dynamic 5 is on
% 3.66/6.40
% 3.66/6.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.66/6.40
% 3.66/6.40
% 3.66/6.40 % ------
% 3.66/6.40 % Current options:
% 3.66/6.40 % ------
% 3.66/6.40
% 3.66/6.40
% 3.66/6.40 %
% 3.66/6.40
% 3.66/6.40 % ------ Proving...
% 3.66/6.40 %
% 3.66/6.40
% 3.66/6.40 % SZS status Theorem for theBenchmark.p
% 3.66/6.40
% 3.66/6.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.66/6.40
% 3.66/6.40
%------------------------------------------------------------------------------