TSTP Solution File: GRP087-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 00:15:56 EDT 2023
% Result : Unsatisfiable 0.47s 0.61s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 32 ( 18 unt; 11 typ; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiply: ( $i * $i ) > $i ).
tff(decl_23,type,
inverse: $i > $i ).
tff(decl_24,type,
a1: $i ).
tff(decl_25,type,
b1: $i ).
tff(decl_26,type,
b2: $i ).
tff(decl_27,type,
a2: $i ).
tff(decl_28,type,
a3: $i ).
tff(decl_29,type,
b3: $i ).
tff(decl_30,type,
c3: $i ).
tff(decl_31,type,
a4: $i ).
tff(decl_32,type,
b4: $i ).
cnf(single_axiom,axiom,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,multiply(multiply(inverse(X2),X3),multiply(multiply(inverse(multiply(X1,X4)),X2),X4))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X4),X3) = multiply(X1,multiply(X4,X2)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_5,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,X2))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_7,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
multiply(multiply(X1,multiply(inverse(X2),X3)),X2) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_9,plain,
multiply(X1,multiply(inverse(multiply(X1,X2)),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_10,plain,
multiply(inverse(X1),multiply(X2,multiply(X3,X1))) = multiply(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_2]),c_0_4]) ).
cnf(c_0_11,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_9]) ).
cnf(c_0_12,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_7]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
prove_these_axioms ).
cnf(c_0_14,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_11]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(b2,multiply(a2,inverse(b2))) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_7]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_7]),c_0_12])]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_19,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_12]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_18,c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 20:23:05 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.47/0.58 start to proof: theBenchmark
% 0.47/0.61 % Version : CSE_E---1.5
% 0.47/0.61 % Problem : theBenchmark.p
% 0.47/0.61 % Proof found
% 0.47/0.61 % SZS status Theorem for theBenchmark.p
% 0.47/0.61 % SZS output start Proof
% See solution above
% 0.47/0.62 % Total time : 0.031000 s
% 0.47/0.62 % SZS output end Proof
% 0.47/0.62 % Total time : 0.034000 s
%------------------------------------------------------------------------------