TSTP Solution File: ALG004-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG004-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 : Wed Aug 30 16:00:03 EDT 2023
% Result : Unsatisfiable 112.00s 112.04s
% Output : CNFRefutation 112.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 41 ( 20 unt; 9 typ; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiply: ( $i * $i ) > $i ).
tff(decl_23,type,
b: $i ).
tff(decl_24,type,
b0: $i ).
tff(decl_25,type,
a: $i ).
tff(decl_26,type,
a0: $i ).
tff(decl_27,type,
d: $i ).
tff(decl_28,type,
c: $i ).
tff(decl_29,type,
d0: $i ).
tff(decl_30,type,
c0: $i ).
cnf(right_cancelaation,axiom,
( X2 = X4
| multiply(X1,X2) != X3
| multiply(X1,X4) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancelaation) ).
cnf(medial_law,axiom,
multiply(multiply(X1,X2),multiply(X3,X4)) = multiply(multiply(X1,X3),multiply(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',medial_law) ).
cnf(prove_quotient_condition3,negated_conjecture,
multiply(b,d0) = multiply(a,c0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition3) ).
cnf(prove_quotient_condition2,negated_conjecture,
multiply(d,b0) = multiply(c,a0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition2) ).
cnf(left_cancellation,axiom,
( X1 = X4
| multiply(X1,X2) != X3
| multiply(X4,X2) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
cnf(prove_quotient_condition1,negated_conjecture,
multiply(b,b0) = multiply(a,a0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition1) ).
cnf(prove_quotient_condition4,negated_conjecture,
multiply(d,d0) != multiply(c,c0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition4) ).
cnf(c_0_7,axiom,
( X2 = X4
| multiply(X1,X2) != X3
| multiply(X1,X4) != X3 ),
right_cancelaation ).
cnf(c_0_8,axiom,
multiply(multiply(X1,X2),multiply(X3,X4)) = multiply(multiply(X1,X3),multiply(X2,X4)),
medial_law ).
cnf(c_0_9,plain,
( X1 = X2
| multiply(X3,X1) != multiply(X3,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
multiply(b,d0) = multiply(a,c0),
prove_quotient_condition3 ).
cnf(c_0_11,negated_conjecture,
multiply(d,b0) = multiply(c,a0),
prove_quotient_condition2 ).
cnf(c_0_12,plain,
multiply(multiply(multiply(X1,X2),multiply(X3,X4)),multiply(X5,X6)) = multiply(multiply(multiply(X1,X3),X5),multiply(multiply(X2,X4),X6)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_13,axiom,
( X1 = X4
| multiply(X1,X2) != X3
| multiply(X4,X2) != X3 ),
left_cancellation ).
cnf(c_0_14,plain,
( multiply(X1,X2) = X3
| multiply(multiply(X4,X1),multiply(X5,X2)) != multiply(multiply(X4,X5),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_15,negated_conjecture,
multiply(multiply(a,X1),multiply(c0,X2)) = multiply(multiply(b,d0),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
multiply(multiply(X1,d),multiply(X2,b0)) = multiply(multiply(X1,X2),multiply(c,a0)),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
multiply(multiply(multiply(X1,X2),multiply(c,a0)),multiply(X3,X4)) = multiply(multiply(multiply(X1,d),X3),multiply(multiply(X2,b0),X4)),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_18,plain,
( X1 = X2
| multiply(X1,X3) != multiply(X2,X3) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( multiply(X1,multiply(c0,X2)) = X3
| multiply(multiply(X4,X1),multiply(multiply(b,d0),multiply(X5,X2))) != multiply(multiply(X4,multiply(a,X5)),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
multiply(multiply(X1,d),multiply(X2,b0)) = multiply(multiply(X1,c),multiply(X2,a0)),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
multiply(b,b0) = multiply(a,a0),
prove_quotient_condition1 ).
cnf(c_0_22,negated_conjecture,
multiply(multiply(multiply(X1,d),X2),multiply(multiply(X3,b0),X4)) = multiply(multiply(multiply(X1,c),X2),multiply(multiply(X3,a0),X4)),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_23,plain,
multiply(multiply(multiply(X1,X2),X3),multiply(multiply(X4,X5),X6)) = multiply(multiply(multiply(X1,X4),X3),multiply(multiply(X2,X5),X6)),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_24,plain,
( multiply(X1,X2) = X3
| multiply(multiply(X1,X4),multiply(X2,X5)) != multiply(X3,multiply(X4,X5)) ),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_25,negated_conjecture,
multiply(multiply(d,X1),multiply(b0,X2)) = multiply(multiply(c,a0),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_26,negated_conjecture,
( multiply(X1,multiply(c0,X2)) = X3
| multiply(multiply(multiply(X4,b),X1),multiply(multiply(c,a0),multiply(d0,X2))) != multiply(multiply(multiply(X4,b),multiply(c,b0)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_8]),c_0_22]),c_0_23]),c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( multiply(X1,X2) = multiply(d,X3)
| multiply(multiply(X1,b0),multiply(X2,X4)) != multiply(multiply(c,a0),multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
multiply(multiply(c,b0),multiply(c0,X1)) = multiply(multiply(c,a0),multiply(d0,X1)),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( multiply(d,X1) = multiply(c,c0)
| multiply(multiply(c,a0),multiply(d0,X2)) != multiply(multiply(c,a0),multiply(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
multiply(d,d0) != multiply(c,c0),
prove_quotient_condition4 ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG004-1 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 05:09:40 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 112.00/112.04 % Version : CSE_E---1.5
% 112.00/112.04 % Problem : theBenchmark.p
% 112.00/112.04 % Proof found
% 112.00/112.04 % SZS status Theorem for theBenchmark.p
% 112.00/112.04 % SZS output start Proof
% See solution above
% 112.00/112.05 % Total time : 111.466000 s
% 112.00/112.05 % SZS output end Proof
% 112.00/112.05 % Total time : 111.473000 s
%------------------------------------------------------------------------------