%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN415+1 : TPTP v9.2.1. Released v2.0.0.
% 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 05:37:03 PM UTC 2026
% Result : Theorem 1.43s 1.77s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 1
% Syntax : Number of formulae : 74 ( 5 unt; 0 def)
% Number of atoms : 300 ( 90 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 380 ( 154 ~; 205 |; 15 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 133 ( 78 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kalish317,conjecture,
( ( ? [X1] : f(X1)
& ! [X2,X3] :
( ( f(X2)
& f(X3) )
=> X2 = X3 ) )
<=> ? [X4] :
( f(X4)
& ! [X5] :
( f(X5)
=> X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish317) ).
fof(c_0_1,negated_conjecture,
~ ( ( ? [X1] : f(X1)
& ! [X2,X3] :
( ( f(X2)
& f(X3) )
=> X2 = X3 ) )
<=> ? [X4] :
( f(X4)
& ! [X5] :
( f(X5)
=> X4 = X5 ) ) ),
inference(assume_negation,[status(cth)],[kalish317]) ).
fof(c_0_2,negated_conjecture,
! [X11,X14,X17,X18,X20] :
( ( f(esk3_1(X14))
| ~ f(X14)
| f(esk1_0)
| ~ f(X11) )
& ( X14 != esk3_1(X14)
| ~ f(X14)
| f(esk1_0)
| ~ f(X11) )
& ( f(esk3_1(X14))
| ~ f(X14)
| f(esk2_0)
| ~ f(X11) )
& ( X14 != esk3_1(X14)
| ~ f(X14)
| f(esk2_0)
| ~ f(X11) )
& ( f(esk3_1(X14))
| ~ f(X14)
| esk1_0 != esk2_0
| ~ f(X11) )
& ( X14 != esk3_1(X14)
| ~ f(X14)
| esk1_0 != esk2_0
| ~ f(X11) )
& ( f(esk5_0)
| f(esk4_0) )
& ( ~ f(X20)
| esk5_0 = X20
| f(esk4_0) )
& ( f(esk5_0)
| ~ f(X17)
| ~ f(X18)
| X17 = X18 )
& ( ~ f(X20)
| esk5_0 = X20
| ~ f(X17)
| ~ f(X18)
| X17 = X18 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( f(esk1_0)
| X1 != esk3_1(X1)
| ~ f(X1)
| ~ f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( f(esk5_0)
| X1 = X2
| ~ f(X1)
| ~ f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( f(esk3_1(X1))
| f(esk1_0)
| ~ f(X1)
| ~ f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( f(esk2_0)
| X1 != esk3_1(X1)
| ~ f(X1)
| ~ f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( f(esk3_1(X1))
| f(esk2_0)
| ~ f(X1)
| ~ f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
( f(esk5_0)
| f(esk1_0)
| ~ f(X1)
| ~ f(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4])]),c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( f(esk5_0)
| f(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( f(esk5_0)
| f(esk2_0)
| ~ f(X1)
| ~ f(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_4])]),c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( f(esk1_0)
| f(esk5_0)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( esk5_0 = X1
| X2 = X3
| ~ f(X1)
| ~ f(X2)
| ~ f(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( f(esk2_0)
| f(esk5_0)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( esk4_0 = X1
| f(esk5_0)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( f(esk5_0)
| f(esk1_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( esk3_1(X1) = esk5_0
| X2 = X3
| f(esk1_0)
| ~ f(X3)
| ~ f(X2)
| ~ f(X4)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( f(esk5_0)
| f(esk2_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( esk5_0 = X1
| f(esk4_0)
| ~ f(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_19,negated_conjecture,
( esk5_0 = X1
| ~ f(esk5_0)
| ~ f(X1) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_12])]) ).
cnf(c_0_20,negated_conjecture,
( esk4_0 = esk1_0
| f(esk5_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( X1 = X2
| f(esk1_0)
| ~ f(X3)
| ~ f(X2)
| ~ f(X1)
| ~ f(X4) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_16])]),c_0_4]) ).
cnf(c_0_22,negated_conjecture,
( esk4_0 = esk2_0
| f(esk5_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( esk3_1(X1) = esk5_0
| f(esk1_0)
| f(esk4_0)
| ~ f(X2)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_5]) ).
cnf(c_0_24,negated_conjecture,
( esk4_0 = esk1_0
| esk5_0 = X1
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( f(esk1_0)
| ~ f(X1)
| ~ f(X2)
| ~ f(X3)
| ~ f(X4) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_21])]),c_0_5]) ).
cnf(c_0_26,negated_conjecture,
( esk4_0 = esk2_0
| esk5_0 = X1
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( f(esk4_0)
| f(esk1_0)
| ~ f(X1)
| ~ f(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_23])]),c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( esk1_0 = esk5_0
| esk4_0 = esk1_0
| ~ f(X1)
| ~ f(X2)
| ~ f(X3)
| ~ f(X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( esk4_0 = esk5_0
| esk4_0 = esk2_0
| f(esk1_0)
| ~ f(X1)
| ~ f(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( esk4_0 = esk1_0
| esk1_0 = esk5_0
| ~ f(X1)
| ~ f(X2)
| ~ f(X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_31,negated_conjecture,
( esk4_0 = esk5_0
| esk1_0 = esk5_0
| esk4_0 = esk2_0
| ~ f(X1)
| ~ f(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( esk1_0 = esk5_0
| esk4_0 = esk1_0
| ~ f(X1)
| ~ f(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_33,negated_conjecture,
( esk4_0 = esk2_0
| esk1_0 = esk5_0
| esk4_0 = esk5_0
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( esk4_0 = esk1_0
| esk1_0 = esk5_0
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_35,negated_conjecture,
( esk4_0 = esk5_0
| esk1_0 = esk5_0
| esk4_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_36,negated_conjecture,
( esk1_0 = esk5_0
| esk4_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_37,negated_conjecture,
( X1 != esk3_1(X1)
| ~ f(X1)
| esk1_0 != esk2_0
| ~ f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_38,negated_conjecture,
( esk2_0 = esk1_0
| esk1_0 = esk5_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( esk1_0 = esk5_0
| esk3_1(X1) != X1
| ~ f(X2)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( f(esk3_1(X1))
| ~ f(X1)
| esk1_0 != esk2_0
| ~ f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_41,negated_conjecture,
( esk1_0 = esk5_0
| f(esk5_0)
| ~ f(esk3_1(X1))
| ~ f(X2)
| ~ f(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_4])]) ).
cnf(c_0_42,negated_conjecture,
( esk1_0 = esk5_0
| f(esk3_1(X1))
| ~ f(X2)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( esk1_0 = esk5_0
| f(esk5_0)
| ~ f(X1)
| ~ f(X2)
| ~ f(X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
( esk1_0 = X1
| f(esk5_0)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_15]) ).
cnf(c_0_45,negated_conjecture,
( esk1_0 = esk5_0
| f(esk5_0)
| ~ f(X1)
| ~ f(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_9]) ).
cnf(c_0_46,negated_conjecture,
( esk1_0 = X1
| esk5_0 = X2
| ~ f(X2)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( esk1_0 = esk5_0
| f(esk1_0)
| ~ f(X1)
| ~ f(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_48,negated_conjecture,
( esk1_0 = esk5_0
| f(esk5_0)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_9]) ).
cnf(c_0_49,negated_conjecture,
( esk1_0 = esk5_0
| esk1_0 = X1
| ~ f(X1)
| ~ f(X2)
| ~ f(X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( esk1_0 = esk5_0
| f(esk5_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_9]) ).
cnf(c_0_51,negated_conjecture,
( esk1_0 = esk5_0
| ~ f(X1)
| ~ f(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,negated_conjecture,
( esk1_0 = esk5_0
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
esk1_0 = esk5_0,
inference(spm,[status(thm)],[c_0_52,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( esk3_1(X1) = esk5_0
| X2 = X3
| f(esk2_0)
| ~ f(X3)
| ~ f(X2)
| ~ f(X4)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_55,negated_conjecture,
f(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_53])]) ).
cnf(c_0_56,negated_conjecture,
( X1 = X2
| f(esk2_0)
| ~ f(X3)
| ~ f(X2)
| ~ f(X1)
| ~ f(X4) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_54])]),c_0_4]) ).
cnf(c_0_57,negated_conjecture,
( esk5_0 = X1
| ~ f(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
( f(esk2_0)
| ~ f(X1)
| ~ f(X2)
| ~ f(X3)
| ~ f(X4) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_56])]),c_0_7]) ).
cnf(c_0_59,negated_conjecture,
( esk2_0 = esk1_0
| f(esk5_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_17]) ).
cnf(c_0_60,negated_conjecture,
( esk2_0 = esk5_0
| ~ f(X1)
| ~ f(X2)
| ~ f(X3)
| ~ f(X4) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( esk2_0 = esk5_0
| f(esk5_0) ),
inference(rw,[status(thm)],[c_0_59,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( esk2_0 = esk5_0
| ~ f(X1)
| ~ f(X2)
| ~ f(X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_63,negated_conjecture,
( esk2_0 = esk5_0
| ~ f(X1)
| ~ f(X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( esk2_0 = esk5_0
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( f(esk3_1(X1))
| esk2_0 != esk5_0
| ~ f(X2)
| ~ f(X1) ),
inference(rw,[status(thm)],[c_0_40,c_0_53]) ).
cnf(c_0_66,negated_conjecture,
esk2_0 = esk5_0,
inference(spm,[status(thm)],[c_0_64,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( esk3_1(X1) != X1
| esk2_0 != esk5_0
| ~ f(X2)
| ~ f(X1) ),
inference(rw,[status(thm)],[c_0_37,c_0_53]) ).
cnf(c_0_68,negated_conjecture,
( f(esk3_1(X1))
| ~ f(X2)
| ~ f(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_69,negated_conjecture,
( esk3_1(X1) != X1
| ~ f(X2)
| ~ f(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_66])]) ).
cnf(c_0_70,negated_conjecture,
( esk3_1(X1) = esk5_0
| ~ f(X2)
| ~ f(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( ~ f(X1)
| ~ f(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70])]),c_0_55])]) ).
cnf(c_0_72,negated_conjecture,
~ f(X1),
inference(spm,[status(thm)],[c_0_71,c_0_55]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_55,c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN415+1 : TPTP v9.2.1. Released v2.0.0.
% 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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 08:33:54 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.43/1.77 % Version : CSE_E---1.7
% 1.43/1.77 % Problem : theBenchmark.p
% 1.43/1.77 % SZS status Theorem for theBenchmark.p
% 1.43/1.77 % SZS output start CNFRefutation
% See solution above
% 1.43/1.77 % Total time : 1.371s
%------------------------------------------------------------------------------