%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU128+1 : 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 : n001.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 05:10:42 PM UTC 2026
% Result : Theorem 1.29s 1.74s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 90 ( 12 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 93 ( 35 ~; 40 |; 12 &)
% ( 3 <=>; 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 67 ( 5 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t19_xboole_1,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_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(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(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
inference(assume_negation,[status(cth)],[t19_xboole_1]) ).
fof(c_0_5,plain,
! [X35,X36,X37,X38,X39] :
( ( ~ subset(X35,X36)
| ~ in(X37,X35)
| in(X37,X36) )
& ( in(esk1_2(X38,X39),X38)
| subset(X38,X39) )
& ( ~ in(esk1_2(X38,X39),X39)
| subset(X38,X39) ) ),
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])])])])])]) ).
fof(c_0_6,negated_conjecture,
( subset(esk5_0,esk6_0)
& subset(esk5_0,esk7_0)
& ~ subset(esk5_0,set_intersection2(esk6_0,esk7_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( in(X44,X41)
| ~ in(X44,X43)
| X43 != set_intersection2(X41,X42) )
& ( in(X44,X42)
| ~ in(X44,X43)
| X43 != set_intersection2(X41,X42) )
& ( ~ in(X45,X41)
| ~ in(X45,X42)
| in(X45,X43)
| X43 != set_intersection2(X41,X42) )
& ( ~ in(esk2_3(X46,X47,X48),X48)
| ~ in(esk2_3(X46,X47,X48),X46)
| ~ in(esk2_3(X46,X47,X48),X47)
| X48 = set_intersection2(X46,X47) )
& ( in(esk2_3(X46,X47,X48),X46)
| in(esk2_3(X46,X47,X48),X48)
| X48 = set_intersection2(X46,X47) )
& ( in(esk2_3(X46,X47,X48),X47)
| in(esk2_3(X46,X47,X48),X48)
| X48 = set_intersection2(X46,X47) ) ),
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])])])])])]) ).
cnf(c_0_8,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
subset(esk5_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( in(X1,esk7_0)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( subset(X1,esk7_0)
| ~ in(esk1_2(X1,esk7_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk1_2(set_intersection2(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
subset(set_intersection2(esk5_0,X1),esk7_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( in(X1,esk7_0)
| ~ in(X1,set_intersection2(esk5_0,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
fof(c_0_20,plain,
! [X50] : set_intersection2(X50,X50) = X50,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
cnf(c_0_21,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( subset(set_intersection2(esk5_0,X1),X2)
| in(esk1_2(set_intersection2(esk5_0,X1),X2),esk7_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_23,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ in(esk1_2(X1,set_intersection2(X2,X3)),X3)
| ~ in(esk1_2(X1,set_intersection2(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( subset(esk5_0,X1)
| in(esk1_2(esk5_0,X1),esk7_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
( subset(esk5_0,set_intersection2(X1,esk7_0))
| ~ in(esk1_2(esk5_0,set_intersection2(X1,esk7_0)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
~ subset(esk5_0,set_intersection2(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_30,negated_conjecture,
~ in(esk1_2(esk5_0,set_intersection2(esk6_0,esk7_0)),esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_14]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU128+1 : 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:45:03 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.29/1.74 % Version : CSE_E---1.7
% 1.29/1.74 % Problem : theBenchmark.p
% 1.29/1.74 % SZS status Theorem for theBenchmark.p
% 1.29/1.74 % SZS output start CNFRefutation
% See solution above
% 1.29/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------