%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU124+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 1.61s 1.81s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 55 ( 11 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 57 ( 21 ~; 25 |; 7 &)
% ( 3 <=>; 1 =>; 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 : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 48 ( 4 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t7_xboole_1,conjecture,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(c_0_4,plain,
! [X75,X76,X77,X78,X79,X80,X81,X82] :
( ( ~ in(X78,X77)
| in(X78,X75)
| in(X78,X76)
| X77 != set_union2(X75,X76) )
& ( ~ in(X79,X75)
| in(X79,X77)
| X77 != set_union2(X75,X76) )
& ( ~ in(X79,X76)
| in(X79,X77)
| X77 != set_union2(X75,X76) )
& ( ~ in(esk2_3(X80,X81,X82),X80)
| ~ in(esk2_3(X80,X81,X82),X82)
| X82 = set_union2(X80,X81) )
& ( ~ in(esk2_3(X80,X81,X82),X81)
| ~ in(esk2_3(X80,X81,X82),X82)
| X82 = set_union2(X80,X81) )
& ( in(esk2_3(X80,X81,X82),X82)
| in(esk2_3(X80,X81,X82),X80)
| in(esk2_3(X80,X81,X82),X81)
| X82 = set_union2(X80,X81) ) ),
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_5,plain,
! [X84,X85,X86,X87,X88] :
( ( ~ subset(X84,X85)
| ~ in(X86,X84)
| in(X86,X85) )
& ( in(esk3_2(X87,X88),X87)
| subset(X87,X88) )
& ( ~ in(esk3_2(X87,X88),X88)
| subset(X87,X88) ) ),
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_6,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] : subset(X1,set_union2(X1,X2)),
inference(assume_negation,[status(cth)],[t7_xboole_1]) ).
cnf(c_0_10,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk3_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,plain,
! [X65,X66] : set_union2(X65,X66) = set_union2(X66,X65),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_13,negated_conjecture,
~ subset(esk9_0,set_union2(esk9_0,esk10_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_14,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
~ subset(esk9_0,set_union2(esk9_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
subset(X1,set_union2(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU124+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:43:36 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.61/1.81 % Version : CSE_E---1.7
% 1.61/1.81 % Problem : theBenchmark.p
% 1.61/1.81 % SZS status Theorem for theBenchmark.p
% 1.61/1.81 % SZS output start CNFRefutation
% See solution above
% 1.61/1.81 % Total time : 1.372s
%------------------------------------------------------------------------------