%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW101+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:29:26 PM UTC 2026
% Result : Theorem 1.37s 1.76s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 30 unt; 0 def)
% Number of atoms : 227 ( 111 equ)
% Maximal formula atoms : 75 ( 3 avg)
% Number of connectives : 236 ( 79 ~; 106 |; 45 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 44 ( 2 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(def_phi,axiom,
! [X1] :
( ( d(X1)
& phi(X1) = X1 )
| ( ~ d(X1)
& phi(X1) = err ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).
fof(def_false2,axiom,
? [X5] :
( false2 = phi(f7(X5))
& ~ ? [X10] : forallprefers(f7(X10),f7(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false2) ).
fof(lazy_impl_axiom3,axiom,
! [X4] : lazy_impl(true,X4) = phi(X4),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).
fof(def_f7,axiom,
! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f7) ).
fof(prop_false,axiom,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_false) ).
fof(lazy_impl_axiom2,axiom,
! [X4] : lazy_impl(false,X4) = true,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).
fof(prop_true,axiom,
! [X1] :
( prop(X1) = true
<=> bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_true) ).
fof(def_bool,axiom,
! [X1] :
( bool(X1)
<=> ( X1 = false
| X1 = true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_bool) ).
fof(false_true_err_in_d,axiom,
( d(true)
& d(false)
& d(err) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).
fof(false1_false2,conjecture,
false1 = false2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false1_false2) ).
fof(def_forallprefers,axiom,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( ~ d(X1)
& d(X2) )
| ( d(X1)
& d(X2)
& ~ bool(X1)
& bool(X2) )
| ( X1 = false
& X2 = true ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).
fof(def_false1,axiom,
false1 = false,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false1) ).
fof(distinct_false_true_err,axiom,
( true != false
& true != err
& false != err ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',distinct_false_true_err) ).
fof(c_0_13,plain,
! [X1] :
( ( d(X1)
& phi(X1) = X1 )
| ( ~ d(X1)
& phi(X1) = err ) ),
inference(fof_simplification,[status(thm)],[def_phi]) ).
fof(c_0_14,plain,
! [X158] :
( false2 = phi(f7(esk7_0))
& ~ forallprefers(f7(X158),f7(esk7_0)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_false2])])])]) ).
fof(c_0_15,plain,
! [X103] : lazy_impl(true,X103) = phi(X103),
inference(variable_rename,[status(thm)],[lazy_impl_axiom3]) ).
fof(c_0_16,plain,
! [X156] : f7(X156) = lazy_impl(prop(X156),X156),
inference(variable_rename,[status(thm)],[def_f7]) ).
fof(c_0_17,plain,
! [X91] :
( ( ~ d(X91)
| d(X91) )
& ( phi(X91) = err
| d(X91) )
& ( ~ d(X91)
| phi(X91) = X91 )
& ( phi(X91) = err
| phi(X91) = X91 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_13])]) ).
fof(c_0_18,plain,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
inference(fof_simplification,[status(thm)],[prop_false]) ).
cnf(c_0_19,plain,
false2 = phi(f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
lazy_impl(true,X1) = phi(X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
f7(X1) = lazy_impl(prop(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( phi(X1) = err
| phi(X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X93] :
( ( prop(X93) != false
| ~ bool(X93) )
& ( bool(X93)
| prop(X93) = false ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
fof(c_0_24,plain,
! [X102] : lazy_impl(false,X102) = true,
inference(variable_rename,[status(thm)],[lazy_impl_axiom2]) ).
cnf(c_0_25,plain,
false2 = lazy_impl(true,lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
( lazy_impl(true,X1) = X1
| lazy_impl(true,X1) = err ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_20]),c_0_20]) ).
fof(c_0_27,plain,
! [X92] :
( ( prop(X92) != true
| bool(X92) )
& ( ~ bool(X92)
| prop(X92) = true ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[prop_true])]) ).
cnf(c_0_28,plain,
( phi(X1) = X1
| ~ d(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
( bool(X1)
| prop(X1) = false ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
lazy_impl(false,X1) = true,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( lazy_impl(prop(esk7_0),esk7_0) = false2
| false2 = err ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
cnf(c_0_32,plain,
( prop(X1) = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X86] :
( ( ~ bool(X86)
| X86 = false
| X86 = true )
& ( X86 != false
| bool(X86) )
& ( X86 != true
| bool(X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_bool])])]) ).
cnf(c_0_34,plain,
( lazy_impl(true,X1) = X1
| ~ d(X1) ),
inference(rw,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_35,plain,
( lazy_impl(true,true) = false2
| bool(esk7_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_30]) ).
cnf(c_0_36,plain,
d(true),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_37,plain,
( lazy_impl(true,esk7_0) = false2
| false2 = err
| ~ bool(esk7_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_38,negated_conjecture,
false1 != false2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[false1_false2])]) ).
cnf(c_0_39,plain,
~ forallprefers(f7(X1),f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_40,plain,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( ~ d(X1)
& d(X2) )
| ( d(X1)
& d(X2)
& ~ bool(X1)
& bool(X2) )
| ( X1 = false
& X2 = true ) ) ),
inference(fof_simplification,[status(thm)],[def_forallprefers]) ).
cnf(c_0_41,plain,
( X1 = false
| X1 = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( false2 = true
| bool(esk7_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_43,plain,
( esk7_0 = false2
| false2 = err
| ~ bool(esk7_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
false1 != false2,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
false1 = false,
inference(split_conjunct,[status(thm)],[def_false1]) ).
cnf(c_0_46,plain,
~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_21]),c_0_21]) ).
fof(c_0_47,plain,
! [X87,X88] :
( ( X87 = false
| d(X87)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| d(X87)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X87 = false
| d(X88)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| d(X88)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X87 = false
| ~ bool(X87)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| ~ bool(X87)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X87 = false
| bool(X88)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| bool(X88)
| ~ d(X87)
| ~ forallprefers(X87,X88) )
& ( X87 = false
| d(X87)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| d(X87)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( X87 = false
| d(X88)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| d(X88)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( X87 = false
| ~ bool(X87)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| ~ bool(X87)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( X87 = false
| bool(X88)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( X88 = true
| bool(X88)
| d(X88)
| ~ forallprefers(X87,X88) )
& ( d(X87)
| ~ d(X88)
| forallprefers(X87,X88) )
& ( ~ d(X87)
| ~ d(X88)
| bool(X87)
| ~ bool(X88)
| forallprefers(X87,X88) )
& ( X87 != false
| X88 != true
| forallprefers(X87,X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
cnf(c_0_48,plain,
( false2 = true
| esk7_0 = true
| esk7_0 = false ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
( false2 = true
| false2 = err
| esk7_0 = false2 ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
false2 != false,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( false2 = err
| ~ forallprefers(lazy_impl(prop(X1),X1),false2) ),
inference(spm,[status(thm)],[c_0_46,c_0_31]) ).
cnf(c_0_52,plain,
( forallprefers(X1,X2)
| X1 != false
| X2 != true ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,plain,
( false2 = err
| false2 = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,plain,
( false2 = err
| lazy_impl(prop(X1),X1) != false ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_55,plain,
( false2 = err
| lazy_impl(true,X1) != false
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_32]) ).
cnf(c_0_56,plain,
( bool(X1)
| X1 != false ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_57,plain,
( false2 = err
| X1 != false
| ~ d(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_34]),c_0_56]) ).
cnf(c_0_58,plain,
d(false),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_59,plain,
false2 = err,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_60,plain,
true != err,
inference(split_conjunct,[status(thm)],[distinct_false_true_err]) ).
cnf(c_0_61,plain,
lazy_impl(true,lazy_impl(prop(esk7_0),esk7_0)) = err,
inference(rw,[status(thm)],[c_0_25,c_0_59]) ).
cnf(c_0_62,plain,
bool(esk7_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_59]),c_0_60]) ).
cnf(c_0_63,plain,
lazy_impl(true,lazy_impl(true,esk7_0)) = err,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_32]),c_0_62])]) ).
cnf(c_0_64,plain,
lazy_impl(true,esk7_0) = err,
inference(spm,[status(thm)],[c_0_63,c_0_26]) ).
cnf(c_0_65,plain,
( esk7_0 = err
| ~ d(esk7_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_64]) ).
cnf(c_0_66,plain,
( esk7_0 = false
| esk7_0 = true ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_59]),c_0_60]) ).
cnf(c_0_67,plain,
esk7_0 = false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_36])]),c_0_60]) ).
cnf(c_0_68,plain,
false != err,
inference(split_conjunct,[status(thm)],[distinct_false_true_err]) ).
cnf(c_0_69,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_67]),c_0_67]),c_0_58])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW101+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:22:59 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.37/1.76 % Version : CSE_E---1.7
% 1.37/1.76 % Problem : theBenchmark.p
% 1.37/1.76 % SZS status Theorem for theBenchmark.p
% 1.37/1.76 % SZS output start CNFRefutation
% See solution above
% 1.37/1.76 % Total time : 1.374s
%------------------------------------------------------------------------------