TSTP Solution File: CAT010-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : CAT010-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 : Wed Aug 30 18:14:07 EDT 2023
% Result : Unsatisfiable 0.23s 0.58s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 20
% Syntax : Number of formulae : 37 ( 26 unt; 11 typ; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 8 >; 11 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 35 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq3: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_25,type,
equivalent: ( $i * $i ) > $i ).
tff(decl_26,type,
true: $i ).
tff(decl_27,type,
there_exists: $i > $i ).
tff(decl_28,type,
domain: $i > $i ).
tff(decl_29,type,
codomain: $i > $i ).
tff(decl_30,type,
compose: ( $i * $i ) > $i ).
tff(decl_31,type,
a: $i ).
tff(decl_32,type,
b: $i ).
cnf(domain_codomain_composition1,axiom,
ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
cnf(ab_exists,hypothesis,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
cnf(ifeq_axiom_001,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
cnf(compose_codomain,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
cnf(composition_implies_domain,axiom,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
cnf(ifeq_axiom_002,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(domain_has_elements,axiom,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
cnf(c_0_9,axiom,
ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
domain_codomain_composition1 ).
cnf(c_0_10,hypothesis,
there_exists(compose(a,b)) = true,
ab_exists ).
cnf(c_0_11,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_12,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose ).
cnf(c_0_13,axiom,
compose(codomain(X1),X1) = X1,
compose_codomain ).
cnf(c_0_14,axiom,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
composition_implies_domain ).
cnf(c_0_15,hypothesis,
domain(a) = codomain(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_16,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_17,plain,
compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,axiom,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
domain_has_elements ).
cnf(c_0_19,hypothesis,
there_exists(codomain(b)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_15]),c_0_16]) ).
cnf(c_0_20,plain,
ifeq2(there_exists(compose(X1,X2)),true,domain(codomain(X1)),codomain(compose(X1,X2))) = codomain(compose(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_21,plain,
ifeq2(there_exists(X1),true,domain(codomain(X1)),codomain(X1)) = codomain(X1),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_22,hypothesis,
there_exists(a) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_19]),c_0_16]) ).
cnf(c_0_23,hypothesis,
domain(codomain(a)) = codomain(compose(a,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_10]),c_0_11]) ).
cnf(c_0_24,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
prove_codomain_of_ab_equals_codomain_of_a ).
cnf(c_0_25,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_11]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : CAT010-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 01:03:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.23/0.56 start to proof: theBenchmark
% 0.23/0.58 % Version : CSE_E---1.5
% 0.23/0.58 % Problem : theBenchmark.p
% 0.23/0.58 % Proof found
% 0.23/0.58 % SZS status Theorem for theBenchmark.p
% 0.23/0.58 % SZS output start Proof
% See solution above
% 0.23/0.58 % Total time : 0.009000 s
% 0.23/0.58 % SZS output end Proof
% 0.23/0.58 % Total time : 0.012000 s
%------------------------------------------------------------------------------