TSTP Solution File: ROB015-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ROB015-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 14:07:18 EDT 2023
% Result : Unsatisfiable 14.00s 14.11s
% Output : CNFRefutation 14.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 12 unt; 9 typ; 0 def)
% Number of atoms : 36 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
negate: $i > $i ).
tff(decl_24,type,
one: $i ).
tff(decl_25,type,
multiply: ( $i * $i ) > $i ).
tff(decl_26,type,
positive_integer: $i > $o ).
tff(decl_27,type,
successor: $i > $i ).
tff(decl_28,type,
e: $i ).
tff(decl_29,type,
d: $i ).
tff(decl_30,type,
k: $i ).
cnf(lemma_3_4,axiom,
( negate(add(X1,negate(add(X2,multiply(X4,add(X1,X3)))))) = X3
| negate(add(X1,negate(X2))) != X3
| ~ positive_integer(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_4) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
cnf(condition,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
cnf(lemma_3_2,axiom,
( X1 = X2
| negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X1,X3)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_2) ).
cnf(k_positive,axiom,
positive_integer(k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_positive) ).
cnf(base_step,axiom,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_step) ).
cnf(c_0_6,axiom,
( negate(add(X1,negate(add(X2,multiply(X4,add(X1,X3)))))) = X3
| negate(add(X1,negate(X2))) != X3
| ~ positive_integer(X4) ),
lemma_3_4 ).
cnf(c_0_7,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_8,plain,
( negate(add(X1,negate(add(X2,multiply(X3,add(X1,X4)))))) = X4
| negate(add(negate(X2),X1)) != X4
| ~ positive_integer(X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
condition ).
cnf(c_0_10,axiom,
( X1 = X2
| negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X1,X3)))) ),
lemma_3_2 ).
cnf(c_0_11,hypothesis,
( negate(add(negate(add(d,negate(e))),negate(add(e,multiply(X1,add(negate(add(d,negate(e))),X2)))))) = X2
| d != X2
| ~ positive_integer(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
positive_integer(k),
k_positive ).
cnf(c_0_13,plain,
( X1 = X2
| negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X3,X1)))) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_14,hypothesis,
( negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X1)))))) = X1
| d != X1 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,hypothesis,
( X1 = negate(e)
| negate(add(negate(e),negate(add(negate(add(d,negate(e))),X1)))) != negate(add(X1,d)) ),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_16,hypothesis,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = d,
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_7]) ).
cnf(c_0_17,axiom,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
base_step ).
cnf(c_0_18,plain,
( negate(add(X1,negate(add(X2,multiply(X3,add(X1,negate(add(X1,negate(X2))))))))) = negate(add(X1,negate(X2)))
| ~ positive_integer(X3) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_19,hypothesis,
negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) != negate(add(d,negate(e))),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_7]),c_0_17]),c_0_7]) ).
cnf(c_0_20,plain,
negate(add(X1,negate(add(X2,multiply(k,add(X1,negate(add(X1,negate(X2))))))))) = negate(add(X1,negate(X2))),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_21,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ROB015-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 07:32:49 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 14.00/14.11 % Version : CSE_E---1.5
% 14.00/14.11 % Problem : theBenchmark.p
% 14.00/14.11 % Proof found
% 14.00/14.11 % SZS status Theorem for theBenchmark.p
% 14.00/14.11 % SZS output start Proof
% See solution above
% 14.00/14.11 % Total time : 13.540000 s
% 14.00/14.11 % SZS output end Proof
% 14.00/14.11 % Total time : 13.544000 s
%------------------------------------------------------------------------------