%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU125+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n031.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 05:10:41 PM UTC 2026
% Result : Theorem 13.15s 8.60s
% Output : CNFRefutation 13.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 7 unt; 0 def)
% Number of atoms : 118 ( 23 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 127 ( 42 ~; 60 |; 17 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 75 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t8_xboole_1,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(c_0_4,plain,
! [X93,X94,X95,X96,X97,X98,X99,X100] :
( ( in(X96,X93)
| ~ in(X96,X95)
| X95 != set_intersection2(X93,X94) )
& ( in(X96,X94)
| ~ in(X96,X95)
| X95 != set_intersection2(X93,X94) )
& ( ~ in(X97,X93)
| ~ in(X97,X94)
| in(X97,X95)
| X95 != set_intersection2(X93,X94) )
& ( ~ in(esk4_3(X98,X99,X100),X100)
| ~ in(esk4_3(X98,X99,X100),X98)
| ~ in(esk4_3(X98,X99,X100),X99)
| X100 = set_intersection2(X98,X99) )
& ( in(esk4_3(X98,X99,X100),X98)
| in(esk4_3(X98,X99,X100),X100)
| X100 = set_intersection2(X98,X99) )
& ( in(esk4_3(X98,X99,X100),X99)
| in(esk4_3(X98,X99,X100),X100)
| X100 = set_intersection2(X98,X99) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
inference(assume_negation,[status(cth)],[t8_xboole_1]) ).
fof(c_0_6,plain,
! [X87,X88,X89,X90,X91] :
( ( ~ subset(X87,X88)
| ~ in(X89,X87)
| in(X89,X88) )
& ( in(esk3_2(X90,X91),X90)
| subset(X90,X91) )
& ( ~ in(esk3_2(X90,X91),X91)
| subset(X90,X91) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(c_0_7,plain,
( in(esk4_3(X1,X2,X3),X2)
| in(esk4_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,plain,
! [X78,X79,X80,X81,X82,X83,X84,X85] :
( ( ~ in(X81,X80)
| in(X81,X78)
| in(X81,X79)
| X80 != set_union2(X78,X79) )
& ( ~ in(X82,X78)
| in(X82,X80)
| X80 != set_union2(X78,X79) )
& ( ~ in(X82,X79)
| in(X82,X80)
| X80 != set_union2(X78,X79) )
& ( ~ in(esk2_3(X83,X84,X85),X83)
| ~ in(esk2_3(X83,X84,X85),X85)
| X85 = set_union2(X83,X84) )
& ( ~ in(esk2_3(X83,X84,X85),X84)
| ~ in(esk2_3(X83,X84,X85),X85)
| X85 = set_union2(X83,X84) )
& ( in(esk2_3(X83,X84,X85),X85)
| in(esk2_3(X83,X84,X85),X83)
| in(esk2_3(X83,X84,X85),X84)
| X85 = set_union2(X83,X84) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).
fof(c_0_9,negated_conjecture,
( subset(esk9_0,esk10_0)
& subset(esk11_0,esk10_0)
& ~ subset(set_union2(esk9_0,esk11_0),esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( set_intersection2(X1,X2) = X2
| in(esk4_3(X1,X2,X2),X2) ),
inference(ef,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
~ subset(set_union2(esk9_0,esk11_0),esk10_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(esk4_3(X1,X2,X3),X1)
| ~ in(esk4_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,plain,
( set_intersection2(X1,X2) = X2
| in(esk4_3(X1,X2,X2),X3)
| ~ subset(X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
subset(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),set_union2(esk9_0,esk11_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_21,plain,
( set_intersection2(X1,X2) = X2
| ~ in(esk4_3(X1,X2,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( set_intersection2(X1,esk9_0) = esk9_0
| in(esk4_3(X1,esk9_0,esk9_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),esk11_0)
| in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),esk9_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
set_intersection2(esk10_0,esk9_0) = esk9_0,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),esk9_0)
| in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),X1)
| ~ subset(esk11_0,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
subset(esk11_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,esk10_0)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),esk10_0)
| in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),esk9_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_31,negated_conjecture,
in(esk3_2(set_union2(esk9_0,esk11_0),esk10_0),esk10_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU125+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.14/0.32 % Computer : n031.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:46:23 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 13.15/8.60 % Version : CSE_E---1.7
% 13.15/8.60 % Problem : theBenchmark.p
% 13.15/8.60 % SZS status Theorem for theBenchmark.p
% 13.15/8.60 % SZS output start CNFRefutation
% See solution above
% 13.15/8.65 % Total time : 6.383s
%------------------------------------------------------------------------------