%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG203+1 : TPTP v9.2.1. Released v2.7.0.
% 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 : n006.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 04:08:11 PM UTC 2026
% Result : Theorem 1.27s 1.74s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 98 ( 34 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 108 ( 37 ~; 29 |; 22 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax3,axiom,
( ? [X1] :
( sorti1(X1)
& op1(X1,X1) = X1 )
& ? [X2] :
( sorti1(X2)
& op1(X2,X2) != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ( ? [X1] :
( sorti2(X1)
& op2(X1,X1) = X1 )
& ? [X2] :
( sorti2(X2)
& op2(X2,X2) != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(ax1,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,negated_conjecture,
! [X33,X34,X35,X36,X37,X38,X39,X40] :
( ( ~ sorti1(X33)
| sorti2(h(X33)) )
& ( ~ sorti2(X34)
| sorti1(j(X34)) )
& ( ~ sorti1(X35)
| ~ sorti1(X36)
| h(op1(X35,X36)) = op2(h(X35),h(X36)) )
& ( ~ sorti2(X37)
| ~ sorti2(X38)
| j(op2(X37,X38)) = op1(j(X37),j(X38)) )
& ( ~ sorti2(X39)
| h(j(X39)) = X39 )
& ( ~ sorti1(X40)
| j(h(X40)) = X40 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
( sorti1(esk1_0)
& op1(esk1_0,esk1_0) = esk1_0
& sorti1(esk2_0)
& op1(esk2_0,esk2_0) != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[ax3])]) ).
fof(c_0_7,plain,
! [X31,X32] :
( ~ sorti2(X31)
| op2(X31,X31) != X31
| ~ sorti2(X32)
| op2(X32,X32) = X32 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).
cnf(c_0_8,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( op2(X2,X2) = X2
| ~ sorti2(X1)
| op2(X1,X1) != X1
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( op2(h(X1),h(esk1_0)) = h(op1(X1,esk1_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
op1(esk1_0,esk1_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( op2(X1,X1) = X1
| ~ sorti2(h(esk1_0))
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_9])]) ).
cnf(c_0_14,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( op2(X1,X1) = X1
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_9])]) ).
fof(c_0_16,plain,
! [X25,X26] :
( ~ sorti1(X25)
| ~ sorti1(X26)
| sorti1(op1(X25,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])]) ).
cnf(c_0_17,negated_conjecture,
( op2(h(X1),h(X1)) = h(X1)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_18,plain,
sorti1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,plain,
( sorti1(op1(X1,X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
op2(h(esk2_0),h(esk2_0)) = h(esk2_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( j(h(op1(X1,X2))) = op1(X1,X2)
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
h(op1(esk2_0,esk2_0)) = h(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_21]),c_0_18])]) ).
cnf(c_0_24,negated_conjecture,
j(h(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,plain,
op1(esk2_0,esk2_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_18])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ALG203+1 : TPTP v9.2.1. Released v2.7.0.
% 0.11/0.13 % 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
% 0.18/0.35 % Computer : n006.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue May 5 10:24:16 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.20/0.36 % start to proof: theBenchmark
% 1.27/1.74 % Version : CSE_E---1.7
% 1.27/1.74 % Problem : theBenchmark.p
% 1.27/1.74 % SZS status Theorem for theBenchmark.p
% 1.27/1.74 % SZS output start CNFRefutation
% See solution above
% 1.27/1.74 % Total time : 1.374s
%------------------------------------------------------------------------------