TSTP Solution File: GRP194+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 : Thu Aug 31 00:17:41 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 42 ( 9 unt; 9 typ; 0 def)
% Number of atoms : 82 ( 14 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 85 ( 36 ~; 35 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% 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 : 47 ( 1 sgn; 22 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
group_member: ( $i * $i ) > $o ).
tff(decl_23,type,
multiply: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
f: $i ).
tff(decl_25,type,
phi: $i > $i ).
tff(decl_26,type,
h: $i ).
tff(decl_27,type,
left_zero: ( $i * $i ) > $o ).
tff(decl_28,type,
f_left_zero: $i ).
tff(decl_29,type,
esk1_1: $i > $i ).
tff(decl_30,type,
esk2_2: ( $i * $i ) > $i ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(homomorphism1,axiom,
! [X2] :
( group_member(X2,f)
=> group_member(phi(X2),h) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
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/sandbox/benchmark/theBenchmark.p',left_zero) ).
fof(surjective,axiom,
! [X2] :
( group_member(X2,h)
=> ? [X3] :
( group_member(X3,f)
& phi(X3) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
fof(left_zero_for_f,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_zero_for_f) ).
fof(prove_left_zero_h,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_zero_h) ).
fof(c_0_7,plain,
! [X5,X6,X7] :
( ~ group_member(X6,X5)
| ~ group_member(X7,X5)
| group_member(multiply(X5,X6,X7),X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[total_function])]) ).
fof(c_0_8,plain,
! [X13,X14] :
( ~ group_member(X13,f)
| ~ group_member(X14,f)
| multiply(h,phi(X13),phi(X14)) = phi(multiply(f,X13,X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism2])]) ).
fof(c_0_9,plain,
! [X12] :
( ~ group_member(X12,f)
| group_member(phi(X12),h) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism1])]) ).
fof(c_0_10,plain,
! [X17,X18,X19,X20,X21] :
( ( group_member(X18,X17)
| ~ left_zero(X17,X18) )
& ( ~ group_member(X19,X17)
| multiply(X17,X18,X19) = X18
| ~ left_zero(X17,X18) )
& ( group_member(esk2_2(X20,X21),X20)
| ~ group_member(X21,X20)
| left_zero(X20,X21) )
& ( multiply(X20,X21,esk2_2(X20,X21)) != X21
| ~ group_member(X21,X20)
| left_zero(X20,X21) ) ),
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_11,plain,
! [X15] :
( ( group_member(esk1_1(X15),f)
| ~ group_member(X15,h) )
& ( phi(esk1_1(X15)) = X15
| ~ group_member(X15,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(multiply(X2,X1,X3),X2)
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,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_8]) ).
cnf(c_0_14,plain,
( group_member(phi(X1),h)
| ~ group_member(X1,f) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( multiply(X2,X3,X1) = X3
| ~ group_member(X1,X2)
| ~ left_zero(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
left_zero(f,f_left_zero),
inference(split_conjunct,[status(thm)],[left_zero_for_f]) ).
cnf(c_0_17,plain,
( group_member(X1,X2)
| ~ left_zero(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( phi(esk1_1(X1)) = X1
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( group_member(esk1_1(X1),f)
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,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_12,c_0_13]),c_0_14]),c_0_14]) ).
cnf(c_0_21,hypothesis,
( multiply(f,f_left_zero,X1) = f_left_zero
| ~ group_member(X1,f) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,hypothesis,
group_member(f_left_zero,f),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_23,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_13,c_0_18]),c_0_19]) ).
cnf(c_0_24,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_20,c_0_21]),c_0_22])]) ).
fof(c_0_25,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_26,plain,
( left_zero(X1,X2)
| multiply(X1,X2,esk2_2(X1,X2)) != X2
| ~ group_member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,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_23,c_0_21]),c_0_22])]),c_0_19]) ).
cnf(c_0_28,hypothesis,
group_member(phi(f_left_zero),h),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,hypothesis,
~ group_member(esk2_2(h,phi(f_left_zero)),h),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_31,plain,
( group_member(esk2_2(X1,X2),X1)
| left_zero(X1,X2)
| ~ group_member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:11:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.008000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.010000 s
%------------------------------------------------------------------------------