%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU309+1 : 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 : n020.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 05:11:26 PM UTC 2026
% Result : Theorem 1.59s 1.89s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 21 unt; 0 def)
% Number of atoms : 113 ( 40 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 43 ~; 37 |; 7 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_pre_topc,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(dt_k2_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(redefinition_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(commutativity_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = subset_intersection2(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t15_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
inference(assume_negation,[status(cth)],[t22_pre_topc]) ).
fof(c_0_12,plain,
! [X154] :
( ~ one_sorted_str(X154)
| cast_as_carrier_subset(X154) = the_carrier(X154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
fof(c_0_13,negated_conjecture,
( one_sorted_str(esk6_0)
& element(esk7_0,powerset(the_carrier(esk6_0)))
& subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),esk7_0)) != esk7_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,plain,
! [X208,X209,X210] :
( ~ element(X209,powerset(X208))
| ~ element(X210,powerset(X208))
| subset_difference(X208,X209,X210) = set_difference(X209,X210) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
fof(c_0_15,plain,
! [X155] :
( ~ one_sorted_str(X155)
| element(cast_as_carrier_subset(X155),powerset(the_carrier(X155))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])]) ).
cnf(c_0_16,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
one_sorted_str(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( subset_difference(X2,X1,X3) = set_difference(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
element(esk7_0,powerset(the_carrier(esk6_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
cast_as_carrier_subset(esk6_0) = the_carrier(esk6_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X205,X206,X207] :
( ~ element(X206,powerset(X205))
| ~ element(X207,powerset(X205))
| subset_intersection2(X205,X206,X207) = set_intersection2(X206,X207) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])]) ).
fof(c_0_23,plain,
! [X224,X225] : set_difference(X224,set_difference(X224,X225)) = set_intersection2(X224,X225),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_24,plain,
! [X151,X152,X153] :
( ~ element(X152,powerset(X151))
| ~ element(X153,powerset(X151))
| subset_intersection2(X151,X152,X153) = subset_intersection2(X151,X153,X152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k5_subset_1])]) ).
fof(c_0_25,plain,
! [X222,X223] :
( ( ~ element(X222,powerset(X223))
| subset(X222,X223) )
& ( ~ subset(X222,X223)
| element(X222,powerset(X223)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_26,plain,
! [X159,X160,X161] :
( ~ element(X160,powerset(X159))
| ~ element(X161,powerset(X159))
| element(subset_difference(X159,X160,X161),powerset(X159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
cnf(c_0_27,negated_conjecture,
( subset_difference(the_carrier(esk6_0),X1,esk7_0) = set_difference(X1,esk7_0)
| ~ element(X1,powerset(the_carrier(esk6_0))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
element(the_carrier(esk6_0),powerset(the_carrier(esk6_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_17])]) ).
cnf(c_0_29,plain,
( subset_intersection2(X2,X1,X3) = set_intersection2(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( subset_intersection2(X2,X1,X3) = subset_intersection2(X2,X3,X1)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,plain,
! [X149,X150] : set_intersection2(X149,X150) = set_intersection2(X150,X149),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_33,negated_conjecture,
subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),subset_difference(the_carrier(esk6_0),cast_as_carrier_subset(esk6_0),esk7_0)) != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( element(subset_difference(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
subset_difference(the_carrier(esk6_0),the_carrier(esk6_0),esk7_0) = set_difference(the_carrier(esk6_0),esk7_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_37,plain,
! [X212,X213] :
( ~ one_sorted_str(X212)
| ~ element(X213,powerset(the_carrier(X212)))
| subset_intersection2(the_carrier(X212),X213,cast_as_carrier_subset(X212)) = X213 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t15_pre_topc])])]) ).
cnf(c_0_38,plain,
( subset_intersection2(X2,X1,X3) = set_difference(X1,set_difference(X1,X3))
| ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( subset_intersection2(the_carrier(esk6_0),X1,esk7_0) = subset_intersection2(the_carrier(esk6_0),esk7_0,X1)
| ~ element(X1,powerset(the_carrier(esk6_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_40,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
subset_difference(the_carrier(esk6_0),the_carrier(esk6_0),subset_difference(the_carrier(esk6_0),the_carrier(esk6_0),esk7_0)) != esk7_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_21]),c_0_21]) ).
cnf(c_0_42,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ subset(X3,X1)
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_43,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_44,negated_conjecture,
element(set_difference(the_carrier(esk6_0),esk7_0),powerset(the_carrier(esk6_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]),c_0_28])]) ).
cnf(c_0_45,plain,
( subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( subset_intersection2(the_carrier(esk6_0),X1,esk7_0) = set_difference(X1,set_difference(X1,esk7_0))
| ~ element(X1,powerset(the_carrier(esk6_0))) ),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_47,negated_conjecture,
subset_intersection2(the_carrier(esk6_0),the_carrier(esk6_0),esk7_0) = subset_intersection2(the_carrier(esk6_0),esk7_0,the_carrier(esk6_0)),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_48,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_30]),c_0_30]) ).
cnf(c_0_49,negated_conjecture,
subset_difference(the_carrier(esk6_0),the_carrier(esk6_0),set_difference(the_carrier(esk6_0),esk7_0)) != esk7_0,
inference(rw,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_50,negated_conjecture,
( subset_difference(the_carrier(esk6_0),the_carrier(esk6_0),X1) = set_difference(the_carrier(esk6_0),X1)
| ~ subset(X1,the_carrier(esk6_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_28]) ).
cnf(c_0_51,negated_conjecture,
subset(set_difference(the_carrier(esk6_0),esk7_0),the_carrier(esk6_0)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( subset_intersection2(the_carrier(esk6_0),X1,the_carrier(esk6_0)) = X1
| ~ element(X1,powerset(the_carrier(esk6_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_21]),c_0_17])]) ).
cnf(c_0_53,negated_conjecture,
subset_intersection2(the_carrier(esk6_0),esk7_0,the_carrier(esk6_0)) = set_difference(esk7_0,set_difference(esk7_0,the_carrier(esk6_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_28]),c_0_47]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
set_difference(esk7_0,set_difference(esk7_0,the_carrier(esk6_0))) != esk7_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),c_0_48]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_19])]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU309+1 : 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
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:56:05 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.59/1.89 % Version : CSE_E---1.7
% 1.59/1.89 % Problem : theBenchmark.p
% 1.59/1.89 % SZS status Theorem for theBenchmark.p
% 1.59/1.89 % SZS output start CNFRefutation
% See solution above
% 1.59/1.89 % Total time : 1.372s
%------------------------------------------------------------------------------