TSTP Solution File: NUM001-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM001-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 10:26:05 EDT 2023
% Result : Unsatisfiable 0.92s 1.03s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 42 ( 16 unt; 6 typ; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 31 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equalish: ( $i * $i ) > $o ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
subtract: ( $i * $i ) > $i ).
tff(decl_25,type,
a: $i ).
tff(decl_26,type,
b: $i ).
tff(decl_27,type,
c: $i ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',transitivity) ).
cnf(addition_inverts_subtraction1,axiom,
equalish(subtract(add(X1,X2),X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',addition_inverts_subtraction1) ).
cnf(commutativity1,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity1) ).
cnf(subtract_substitution1,axiom,
( equalish(X3,subtract(X2,X4))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',subtract_substitution1) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',addition_inverts_subtraction2) ).
cnf(commutativity_of_addition,axiom,
equalish(add(X1,X2),add(X2,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity_of_addition) ).
cnf(add_substitution2,axiom,
( equalish(X3,add(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,add(X4,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',add_substitution2) ).
cnf(subtract_substitution2,axiom,
( equalish(X3,subtract(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X4,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',subtract_substitution2) ).
cnf(associativity_of_addition,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',associativity_of_addition) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_10,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity ).
cnf(c_0_11,axiom,
equalish(subtract(add(X1,X2),X2),X1),
addition_inverts_subtraction1 ).
cnf(c_0_12,plain,
( equalish(X1,X2)
| ~ equalish(X1,subtract(add(X2,X3),X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
commutativity1 ).
cnf(c_0_14,plain,
equalish(add(subtract(X1,X2),X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
( equalish(X3,subtract(X2,X4))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X1,X4)) ),
subtract_substitution1 ).
cnf(c_0_16,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
addition_inverts_subtraction2 ).
cnf(c_0_17,plain,
( equalish(X1,X2)
| ~ equalish(X1,add(subtract(X2,X3),X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_18,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_addition ).
cnf(c_0_19,plain,
( equalish(X1,subtract(X2,X3))
| ~ equalish(add(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
equalish(add(X1,subtract(X2,X1)),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
( equalish(X3,add(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,add(X4,X1)) ),
add_substitution2 ).
cnf(c_0_22,plain,
( equalish(X1,subtract(X2,X3))
| ~ equalish(add(X1,X3),X4)
| ~ equalish(X4,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_23,plain,
( equalish(X1,X2)
| ~ equalish(X1,add(X3,subtract(X2,X3))) ),
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_24,plain,
( equalish(add(X1,X2),add(X2,X3))
| ~ equalish(X1,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_25,axiom,
( equalish(X3,subtract(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X4,X1)) ),
subtract_substitution2 ).
cnf(c_0_26,plain,
( equalish(X1,subtract(X2,X3))
| ~ equalish(add(X3,X1),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_27,plain,
( equalish(add(X1,X2),X3)
| ~ equalish(X1,subtract(X3,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( equalish(X1,subtract(add(X1,X2),X3))
| ~ equalish(X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_29,plain,
( equalish(X1,X2)
| ~ equalish(add(X3,X1),add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_26]) ).
cnf(c_0_30,plain,
( equalish(add(X1,X2),add(X1,X3))
| ~ equalish(X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
associativity_of_addition ).
cnf(c_0_33,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
prove_equation ).
cnf(c_0_34,plain,
equalish(add(add(X1,X2),X3),add(X1,add(X2,X3))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 11:07:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.92/1.03 % Version : CSE_E---1.5
% 0.92/1.03 % Problem : theBenchmark.p
% 0.92/1.03 % Proof found
% 0.92/1.03 % SZS status Theorem for theBenchmark.p
% 0.92/1.03 % SZS output start Proof
% See solution above
% 0.92/1.03 % Total time : 0.463000 s
% 0.92/1.03 % SZS output end Proof
% 0.92/1.03 % Total time : 0.465000 s
%------------------------------------------------------------------------------