TSTP Solution File: ROB016-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ROB016-1 : 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 : n017.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 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 14 unt; 9 typ; 0 def)
% Number of atoms : 22 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 17 ( 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,
d: $i ).
tff(decl_29,type,
e: $i ).
tff(decl_30,type,
k: $i ).
cnf(robbins_axiom,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
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(d,e)) = negate(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
cnf(lemma_3_6,axiom,
( negate(add(X1,multiply(X3,add(X2,negate(add(X2,negate(X1))))))) = negate(X1)
| negate(add(negate(X1),negate(add(X2,negate(X1))))) != X2
| ~ positive_integer(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_6) ).
cnf(k_positive,axiom,
positive_integer(k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_positive) ).
cnf(prove_result,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_result) ).
cnf(c_0_6,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
robbins_axiom ).
cnf(c_0_7,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_8,hypothesis,
negate(add(d,e)) = negate(e),
condition ).
cnf(c_0_9,plain,
negate(add(negate(add(X1,X2)),negate(add(X2,negate(X1))))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,hypothesis,
negate(add(e,d)) = negate(e),
inference(rw,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_11,axiom,
( negate(add(X1,multiply(X3,add(X2,negate(add(X2,negate(X1))))))) = negate(X1)
| negate(add(negate(X1),negate(add(X2,negate(X1))))) != X2
| ~ positive_integer(X3) ),
lemma_3_6 ).
cnf(c_0_12,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
( negate(add(e,multiply(X1,add(d,negate(add(d,negate(e))))))) = negate(e)
| ~ positive_integer(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
positive_integer(k),
k_positive ).
cnf(c_0_15,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
prove_result ).
cnf(c_0_16,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : ROB016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n017.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 06:21:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.023000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.026000 s
%------------------------------------------------------------------------------