%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU139+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 : n025.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 05:10:44 PM UTC 2026
% Result : Theorem 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 19)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(t60_xboole_1,conjecture,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(i_0_6,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_7,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_8,negated_conjecture,
~ ! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
inference(assume_negation,[status(cth)],[t60_xboole_1]) ).
fof(i_0_9,plain,
! [X17,X18] :
( ( subset(X17,X18)
| X17 != X18 )
& ( subset(X18,X17)
| X17 != X18 )
& ( ~ subset(X17,X18)
| ~ subset(X18,X17)
| X17 = X18 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_10,plain,
! [X15,X16] :
( ~ proper_subset(X15,X16)
| ~ proper_subset(X16,X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6])]) ).
fof(i_0_11,plain,
! [X19,X20] :
( ( subset(X19,X20)
| ~ proper_subset(X19,X20) )
& ( X19 != X20
| ~ proper_subset(X19,X20) )
& ( ~ subset(X19,X20)
| X19 = X20
| proper_subset(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_12,plain,
! [X21] : ~ proper_subset(X21,X21),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_7])]) ).
fof(i_0_13,plain,
! [X22] : subset(X22,X22),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_14,negated_conjecture,
( subset(esk1_0,esk2_0)
& proper_subset(esk2_0,esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])])]) ).
cnf(i_0_15,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_16,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_17,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_18,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_19,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_20,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_21,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_22,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_23,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_25,negated_conjecture,
proper_subset(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_26,axiom,
X1 = X1 ).
cnf(i_0_27,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_28,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_29,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_30,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_31,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_32,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_26_001,axiom,
X1 = X1 ).
cnf(i_0_27_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_28_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_29_004,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_30_005,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_31_006,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_32_007,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_33,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[19]) ).
cnf(i_0_34,plain,
subset(X1,X1),
inference(equality_inference,[],[21]) ).
cnf(i_0_35,plain,
subset(X1,X1),
inference(equality_inference,[],[22]) ).
cnf(i_0_36,plain,
~ proper_subset(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_25,i_0_16]) ).
cnf(i_0_37,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_38,plain,
subset(esk2_0,esk1_0),
inference(scs_inference,[],[i_0_25,i_0_16,i_0_18]) ).
cnf(i_0_39,plain,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_40,plain,
esk2_0 != esk1_0,
inference(scs_inference,[],[i_0_25,i_0_16,i_0_18,i_0_19]) ).
cnf(i_0_41,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_42,plain,
esk1_0 = esk2_0,
inference(scs_inference,[],[i_0_24,i_0_25,i_0_16,i_0_18,i_0_19,i_0_15]) ).
cnf(i_0_43,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_44,plain,
$false,
inference(scs_inference,[],[i_0_24,i_0_25,i_0_20,i_0_16,i_0_18,i_0_19,i_0_15,i_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU139+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
% 0.14/0.32 % Computer : n025.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 02:44:43 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Theorem for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------