TSTP Solution File: GRP402-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP402-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 00:18:50 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 19 unt; 5 typ; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 7 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiply: ( $i * $i ) > $i ).
tff(decl_23,type,
commutator: ( $i * $i ) > $i ).
tff(decl_24,type,
a: $i ).
tff(decl_25,type,
b: $i ).
tff(decl_26,type,
c: $i ).
cnf(left_cancellation,axiom,
( X2 = X3
| multiply(X1,X2) != multiply(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
cnf(commutator,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
cnf(nilpotency,axiom,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nilpotency) ).
cnf(prove_commutator_is_associative,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
cnf(c_0_5,axiom,
( X2 = X3
| multiply(X1,X2) != multiply(X1,X3) ),
left_cancellation ).
cnf(c_0_6,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
commutator ).
cnf(c_0_7,plain,
( X1 = multiply(X2,commutator(X2,X3))
| multiply(X3,X1) != multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_9,plain,
multiply(X1,commutator(X1,X1)) = X1,
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_10,axiom,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
nilpotency ).
cnf(c_0_11,plain,
( X1 = X2
| multiply(X3,multiply(X4,X1)) != multiply(X3,multiply(X4,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
multiply(X1,multiply(commutator(X1,X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( X1 = X2
| multiply(commutator(X3,X4),X1) != multiply(X2,commutator(X3,X4)) ),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_14,plain,
( X1 = commutator(X2,X2)
| multiply(X3,multiply(X2,X1)) != multiply(X3,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_15,plain,
multiply(X1,multiply(X2,commutator(X1,X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,plain,
( multiply(X1,commutator(X1,commutator(X2,X3))) = X4
| multiply(X1,commutator(X2,X3)) != multiply(X4,commutator(X2,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_6]) ).
cnf(c_0_17,plain,
commutator(X1,X1) = commutator(X2,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
multiply(X1,commutator(X1,commutator(X2,X3))) = X1,
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
( X1 = commutator(X2,X3)
| multiply(X3,multiply(X2,X1)) != multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_6]) ).
cnf(c_0_20,plain,
multiply(X1,commutator(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
prove_commutator_is_associative ).
cnf(c_0_22,plain,
commutator(X1,commutator(X2,X3)) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_23,plain,
( X1 = commutator(commutator(X2,X3),X4)
| multiply(X4,multiply(X1,commutator(X2,X3))) != multiply(commutator(X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_24,plain,
multiply(commutator(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,a),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
commutator(X1,X1) = commutator(commutator(X2,X3),X4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_10]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_25,c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP402-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 21:34:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.64 % Version : CSE_E---1.5
% 0.20/0.64 % Problem : theBenchmark.p
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark.p
% 0.20/0.64 % SZS output start Proof
% See solution above
% 0.20/0.65 % Total time : 0.055000 s
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time : 0.057000 s
%------------------------------------------------------------------------------