%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP194+1 : TPTP v9.2.1. Released v2.0.0.
% 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 : n019.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 04:24:47 PM UTC 2026
% Result : Theorem 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 92 ( 14 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 41 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 1 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_zero,axiom,
! [X1,X2] :
( left_zero(X1,X2)
<=> ( group_member(X2,X1)
& ! [X3] :
( group_member(X3,X1)
=> multiply(X1,X2,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
fof(homomorphism1,axiom,
! [X2] :
( group_member(X2,f)
=> group_member(phi(X2),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(total_function,axiom,
! [X1,X2,X3] :
( ( group_member(X2,X1)
& group_member(X3,X1) )
=> group_member(multiply(X1,X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP007+0.ax',total_function) ).
fof(homomorphism2,axiom,
! [X2,X3] :
( ( group_member(X2,f)
& group_member(X3,f) )
=> multiply(h,phi(X2),phi(X3)) = phi(multiply(f,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(surjective,axiom,
! [X2] :
( group_member(X2,h)
=> ? [X3] :
( group_member(X3,f)
& phi(X3) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(left_zero_for_f,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
fof(prove_left_zero_h,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
fof(c_0_7,plain,
! [X32,X33,X34,X35,X36] :
( ( group_member(X33,X32)
| ~ left_zero(X32,X33) )
& ( ~ group_member(X34,X32)
| multiply(X32,X33,X34) = X33
| ~ left_zero(X32,X33) )
& ( group_member(esk2_2(X35,X36),X35)
| ~ group_member(X36,X35)
| left_zero(X35,X36) )
& ( multiply(X35,X36,esk2_2(X35,X36)) != X36
| ~ group_member(X36,X35)
| left_zero(X35,X36) ) ),
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)],[left_zero])])])])])]) ).
fof(c_0_8,plain,
! [X27] :
( ~ group_member(X27,f)
| group_member(phi(X27),h) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism1])]) ).
fof(c_0_9,plain,
! [X20,X21,X22] :
( ~ group_member(X21,X20)
| ~ group_member(X22,X20)
| group_member(multiply(X20,X21,X22),X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[total_function])]) ).
fof(c_0_10,plain,
! [X28,X29] :
( ~ group_member(X28,f)
| ~ group_member(X29,f)
| multiply(h,phi(X28),phi(X29)) = phi(multiply(f,X28,X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism2])]) ).
fof(c_0_11,plain,
! [X30] :
( ( group_member(esk1_1(X30),f)
| ~ group_member(X30,h) )
& ( phi(esk1_1(X30)) = X30
| ~ group_member(X30,h) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[surjective])])])]) ).
cnf(c_0_12,plain,
( group_member(esk2_2(X1,X2),X1)
| left_zero(X1,X2)
| ~ group_member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( group_member(phi(X1),h)
| ~ group_member(X1,f) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( group_member(X1,X2)
| ~ left_zero(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,hypothesis,
left_zero(f,f_left_zero),
inference(split_conjunct,[status(thm)],[left_zero_for_f]) ).
fof(c_0_16,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_left_zero_h])]) ).
cnf(c_0_17,plain,
( group_member(multiply(X2,X1,X3),X2)
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2))
| ~ group_member(X1,f)
| ~ group_member(X2,f) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( multiply(X2,X3,X1) = X3
| ~ group_member(X1,X2)
| ~ left_zero(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
( group_member(esk1_1(X1),f)
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( left_zero(h,phi(X1))
| group_member(esk2_2(h,phi(X1)),h)
| ~ group_member(X1,f) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_22,hypothesis,
group_member(f_left_zero,f),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( group_member(phi(multiply(f,X1,X2)),h)
| ~ group_member(X2,f)
| ~ group_member(X1,f) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13]),c_0_13]) ).
cnf(c_0_25,hypothesis,
( multiply(f,f_left_zero,X1) = f_left_zero
| ~ group_member(X1,f) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_26,plain,
( left_zero(f,esk1_1(X1))
| group_member(esk2_2(f,esk1_1(X1)),f)
| ~ group_member(X1,h) ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_27,hypothesis,
group_member(esk2_2(h,phi(f_left_zero)),h),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_28,plain,
( phi(esk1_1(X1)) = X1
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,hypothesis,
( group_member(phi(f_left_zero),h)
| ~ group_member(X1,f) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22])]) ).
cnf(c_0_30,hypothesis,
( left_zero(f,esk1_1(esk2_2(h,phi(f_left_zero))))
| group_member(esk2_2(f,esk1_1(esk2_2(h,phi(f_left_zero)))),f) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( phi(multiply(f,X1,esk1_1(X2))) = multiply(h,phi(X1),X2)
| ~ group_member(X1,f)
| ~ group_member(X2,h) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_20]) ).
cnf(c_0_32,hypothesis,
( left_zero(f,esk1_1(esk2_2(h,phi(f_left_zero))))
| group_member(phi(f_left_zero),h) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( left_zero(X1,X2)
| multiply(X1,X2,esk2_2(X1,X2)) != X2
| ~ group_member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_34,hypothesis,
( multiply(h,phi(f_left_zero),X1) = phi(f_left_zero)
| ~ group_member(X1,h) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_22])]),c_0_20]) ).
cnf(c_0_35,hypothesis,
group_member(phi(f_left_zero),h),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_32]),c_0_29]) ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_27])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP194+1 : TPTP v9.2.1. Released v2.0.0.
% 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
% 0.16/0.33 % Computer : n019.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:27:59 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Theorem for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------