%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:18:32 PM UTC 2026
% Result : Unsatisfiable 42.94s 5.89s
% Output : Proof 42.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 34 unt; 0 def)
% Number of atoms : 122 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 122 ( 66 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 144 ( 6 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f12,axiom,
( product(B,A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_commutativity) ).
fof(f12_nnf,plain,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f9,axiom,
product(A,B,multiply(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
fof(f9_nnf,plain,
! [A,B] : product(A,B,multiply(A,B)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] : product(A,B,multiply(A,B)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h9,plain,
product(V0,V1,multiply(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi9]) ).
cnf(f17,axiom,
( divides(A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_divisible_by_operand) ).
fof(f17_nnf,plain,
! [A,B,C] :
( divides(A,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C] :
( divides(A,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
ifeq(product(X0,X1,X2),true,divides(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h71,plain,
divides(V0,multiply(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi17,h9]) ).
cnf(h4,plain,
divides(V0,multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi9]) ).
cnf(f18,axiom,
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',primes_lemma1) ).
fof(f18_nnf,plain,
! [A,B,C] :
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C] :
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(divides(X0,X1),true,ifeq(product(X2,X2,X1),true,ifeq(prime(X0),true,divides(X0,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f19,hypothesis,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
fof(f19_nnf,plain,
prime(a),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
prime(a),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
prime(a) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h18,plain,
divides(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi18,h4,hi9,hi19]) ).
cnf(f16,axiom,
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_implies_product) ).
fof(f16_nnf,plain,
! [A,B] :
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( product(X0,second_divided_by_1st(X0,X1),X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(divides(X0,X1),true,product(X0,second_divided_by_1st(X0,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h22,plain,
product(a,second_divided_by_1st(a,a),a) = true,
inference(hyper_resolution,[status(thm)],[hi16,h18]) ).
cnf(f11,axiom,
( product(F,E,C)
| ~ product(F,D,A)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_associativity2) ).
fof(f11_nnf,plain,
! [A,B,C,D,E,F] :
( product(F,E,C)
| ~ product(F,D,A)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,C,D,E,F] :
( product(F,E,C)
| ~ product(F,D,A)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( product(X5,X4,X2)
| ~ product(X5,X3,X0)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h228,plain,
product(a,multiply(V0,second_divided_by_1st(a,a)),multiply(V0,a)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h9,h9,h22]) ).
cnf(f13,axiom,
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X2),true,equalish(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h15436,plain,
equalish(multiply(V0,second_divided_by_1st(a,a)),V0) = true,
inference(hyper_resolution,[status(thm)],[hi13,h228,h9]) ).
cnf(f6,axiom,
( divides(C,A)
| ~ divides(C,B)
| ~ equalish(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_substitution1) ).
fof(f6_nnf,plain,
! [B,A,C] :
( divides(C,A)
| ~ divides(C,B)
| ~ equalish(B,A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,A,C] :
( divides(C,A)
| ~ divides(C,B)
| ~ equalish(B,A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( divides(X2,X1)
| ~ divides(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(equalish(X0,X1),true,ifeq(divides(X2,X0),true,divides(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h15962,plain,
divides(second_divided_by_1st(a,a),V0) = true,
inference(hyper_resolution,[status(thm)],[hi6,h15436,h71]) ).
cnf(f23,negated_conjecture,
( ~ divides(A,b)
| ~ divides(A,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
fof(f23_nnf,plain,
! [A] :
( ~ divides(A,b)
| ~ divides(A,c) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A] :
( ~ divides(A,b)
| ~ divides(A,c) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ divides(X0,b)
| ~ divides(X0,c) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi23,negated_conjecture,
ifeq(divides(X0,c),true,ifeq(divides(X0,b),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi23,h15962,h15962]) ).
cnf(t3511,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f22,hypothesis,
~ product(a,e,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_squared_is_not_b_squared) ).
fof(f22_nnf,plain,
~ product(a,e,d),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ product(a,e,d),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ product(a,e,d),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c22,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3511]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 02:42:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 42.94/5.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.94/5.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------