TSTP Solution File: NUN133-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUN133-1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 12:46:07 EDT 2023
% Result : Unsatisfiable 274.13s 274.00s
% Output : CNFRefutation 274.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 45 ( 37 unt; 8 typ; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
'+': ( $i * $i ) > $i ).
tff(decl_23,type,
times: ( $i * $i ) > $i ).
tff(decl_24,type,
zero: $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
s: $i > $i ).
tff(decl_27,type,
sum: $i > $i ).
tff(decl_28,type,
cubes: $i > $i ).
tff(decl_29,type,
a: $i ).
cnf(sum_s,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_s) ).
cnf(plus_comm,axiom,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_comm) ).
cnf(goal,negated_conjecture,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(cubes_s,axiom,
cubes(s(X1)) = '+'(times(s(X1),times(s(X1),s(X1))),cubes(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cubes_s) ).
cnf(times_s,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_s) ).
cnf(plus_sum,axiom,
'+'(sum(X1),sum(X1)) = times(X1,s(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_sum) ).
cnf(induction_hypothesis,axiom,
times(sum(a),sum(a)) = cubes(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction_hypothesis) ).
cnf(plus_assoc,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_assoc) ).
cnf(distr,axiom,
times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr) ).
cnf(distr_001,axiom,
times('+'(X1,X2),X3) = '+'(times(X1,X3),times(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr_001) ).
cnf(times_one,axiom,
times(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
cnf(times_comm,axiom,
times(X1,X2) = times(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_comm) ).
cnf(times_assoc,axiom,
times(X1,times(X2,X3)) = times(times(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_assoc) ).
cnf(c_0_13,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
sum_s ).
cnf(c_0_14,axiom,
'+'(X1,X2) = '+'(X2,X1),
plus_comm ).
cnf(c_0_15,negated_conjecture,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
goal ).
cnf(c_0_16,plain,
sum(s(X1)) = '+'(sum(X1),s(X1)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
cubes(s(X1)) = '+'(times(s(X1),times(s(X1),s(X1))),cubes(X1)),
cubes_s ).
cnf(c_0_18,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
times_s ).
cnf(c_0_19,axiom,
'+'(sum(X1),sum(X1)) = times(X1,s(X1)),
plus_sum ).
cnf(c_0_20,negated_conjecture,
cubes(s(a)) != times('+'(sum(a),s(a)),'+'(sum(a),s(a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_21,plain,
cubes(s(X1)) = '+'(cubes(X1),'+'('+'('+'(sum(X1),sum(X1)),s(X1)),times(X1,'+'('+'(sum(X1),sum(X1)),s(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_14]),c_0_18]),c_0_14]) ).
cnf(c_0_22,axiom,
times(sum(a),sum(a)) = cubes(a),
induction_hypothesis ).
cnf(c_0_23,negated_conjecture,
times('+'(sum(a),s(a)),'+'(sum(a),s(a))) != '+'(times(sum(a),sum(a)),'+'('+'('+'(sum(a),sum(a)),s(a)),times(a,'+'('+'(sum(a),sum(a)),s(a))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
plus_assoc ).
cnf(c_0_25,axiom,
times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
distr ).
cnf(c_0_26,axiom,
times('+'(X1,X2),X3) = '+'(times(X1,X3),times(X2,X3)),
distr_001 ).
cnf(c_0_27,axiom,
times(X1,one) = X1,
times_one ).
cnf(c_0_28,axiom,
times(X1,X2) = times(X2,X1),
times_comm ).
cnf(c_0_29,axiom,
times(X1,times(X2,X3)) = times(times(X1,X2),X3),
times_assoc ).
cnf(c_0_30,negated_conjecture,
'+'(sum(a),'+'(times(a,sum(a)),'+'(times(sum(a),sum(a)),'+'(sum(a),'+'(sum(a),'+'(s(a),times(sum(a),s(a)))))))) != '+'(times(sum(a),sum(a)),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),s(a)))))))),
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)],[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)],[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_23,c_0_24]),c_0_24]),c_0_24]),c_0_25]),c_0_26]),c_0_18]),c_0_14]),c_0_24]),c_0_26]),c_0_18]),c_0_19]),c_0_14]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_25]),c_0_25]),c_0_19]),c_0_14]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_31,plain,
s(X1) = '+'(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_27]) ).
cnf(c_0_32,plain,
'+'(X1,X2) = '+'(X2,X1),
c_0_14 ).
cnf(c_0_33,plain,
times(X1,X2) = times(X2,X1),
c_0_28 ).
cnf(c_0_34,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
c_0_24 ).
cnf(c_0_35,plain,
times(times(X1,X2),X3) = times(X1,times(X2,X3)),
c_0_29 ).
cnf(c_0_36,negated_conjecture,
$false,
inference(ar,[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_25]),c_0_27]),c_0_28]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_31]),c_0_14]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_32,c_0_33,c_0_34,c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN133-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 09:53:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 274.13/274.00 % Version : CSE_E---1.5
% 274.13/274.00 % Problem : theBenchmark.p
% 274.13/274.00 % Proof found
% 274.13/274.00 % SZS status Theorem for theBenchmark.p
% 274.13/274.00 % SZS output start Proof
% See solution above
% 274.13/274.01 % Total time : 273.453000 s
% 274.13/274.01 % SZS output end Proof
% 274.13/274.01 % Total time : 273.469000 s
%------------------------------------------------------------------------------