TSTP Solution File: GRP748-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP748-2 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 00:23:34 EDT 2023
% Result : Unsatisfiable 0.52s 0.88s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 34 unt; 8 typ; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ld: ( $i * $i ) > $i ).
tff(decl_23,type,
mult: ( $i * $i ) > $i ).
tff(decl_24,type,
rd: ( $i * $i ) > $i ).
tff(decl_25,type,
unit: $i ).
tff(decl_26,type,
i: $i > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
cnf(f11,axiom,
( mult(X1,X2) = mult(X2,X1)
| mult(i(X1),mult(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
cnf(f01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(f08,axiom,
mult(mult(X1,X2),i(X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
cnf(f09,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
cnf(f06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
cnf(f07,axiom,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
cnf(f10,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
cnf(f02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(goals,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_9,axiom,
( mult(X1,X2) = mult(X2,X1)
| mult(i(X1),mult(X1,X2)) = X2 ),
f11 ).
cnf(c_0_10,axiom,
mult(X1,ld(X1,X2)) = X2,
f01 ).
cnf(c_0_11,axiom,
mult(mult(X1,X2),i(X2)) = X1,
f08 ).
cnf(c_0_12,plain,
( ld(X1,X2) = mult(i(X1),X2)
| mult(ld(X1,X2),X1) = X2 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ld(X1,X2) = mult(i(X1),X2)
| ld(X1,X2) = mult(X2,i(X1)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( ld(X1,X2) = mult(X2,i(X1))
| mult(i(X1),X2) != mult(X2,i(X1)) ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_15,axiom,
mult(X1,i(X1)) = unit,
f09 ).
cnf(c_0_16,axiom,
mult(unit,X1) = X1,
f06 ).
cnf(c_0_17,axiom,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
f07 ).
cnf(c_0_18,axiom,
mult(i(X1),X1) = unit,
f10 ).
cnf(c_0_19,plain,
( mult(X1,mult(X2,i(X1))) = X2
| mult(i(X1),X2) != mult(X2,i(X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_20,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_16]) ).
cnf(c_0_21,axiom,
ld(X1,mult(X1,X2)) = X2,
f02 ).
cnf(c_0_22,plain,
mult(i(X1),mult(mult(X1,X2),X1)) = mult(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).
cnf(c_0_23,plain,
ld(i(X1),X2) = mult(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_20]),c_0_10])]) ).
cnf(c_0_24,plain,
ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_23]) ).
cnf(c_0_26,plain,
mult(mult(X1,mult(mult(X2,X3),X2)),i(X2)) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_27,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(rw,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_28,plain,
mult(X1,i(mult(X2,X1))) = i(X2),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_29,plain,
mult(mult(X1,i(X2)),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_26]),c_0_18]),c_0_16]),c_0_20]),c_0_27]) ).
cnf(c_0_30,plain,
i(mult(X1,X2)) = mult(i(X2),i(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_31,plain,
mult(mult(X1,i(X2)),mult(mult(X2,X3),X1)) = mult(X1,mult(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_30]),c_0_20]) ).
cnf(c_0_32,plain,
mult(mult(X1,mult(X2,X1)),i(X1)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_27]) ).
cnf(c_0_33,plain,
mult(mult(X1,i(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_34,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
goals ).
cnf(c_0_35,plain,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_20]) ).
cnf(c_0_36,plain,
mult(mult(X1,X2),i(X1)) = mult(X1,mult(X2,i(X1))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
inference(rw,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_38,plain,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_35]),c_0_36]),c_0_11]),c_0_27]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP748-2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % 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 21:39:10 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.52/0.88 % Version : CSE_E---1.5
% 0.52/0.88 % Problem : theBenchmark.p
% 0.52/0.88 % Proof found
% 0.52/0.88 % SZS status Theorem for theBenchmark.p
% 0.52/0.88 % SZS output start Proof
% See solution above
% 0.52/0.89 % Total time : 0.327000 s
% 0.52/0.89 % SZS output end Proof
% 0.52/0.89 % Total time : 0.330000 s
%------------------------------------------------------------------------------