%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 : Thu Sep 24 08:54:53 AM UTC 2026
% Result : Unsatisfiable 120.11s 145.46s
% Output : Proof 120.27s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_inverse_substitution,axiom,
( equalish(additive_inverse(X),additive_inverse(Y))
| ~ equalish(X,Y) ),
file('theBenchmark.p',additive_inverse_substitution) ).
cnf(add_substitution1,axiom,
( equalish(add(X,W),add(Y,W))
| ~ equalish(X,Y) ),
file('theBenchmark.p',add_substitution1) ).
cnf(sum_substitution1,axiom,
( sum(Y,W,Z)
| ~ sum(X,W,Z)
| ~ equalish(X,Y) ),
file('theBenchmark.p',sum_substitution1) ).
cnf(sum_substitution2,axiom,
( sum(W,Y,Z)
| ~ sum(W,X,Z)
| ~ equalish(X,Y) ),
file('theBenchmark.p',sum_substitution2) ).
cnf(sum_substitution3,axiom,
( sum(W,Z,Y)
| ~ sum(W,Z,X)
| ~ equalish(X,Y) ),
file('theBenchmark.p',sum_substitution3) ).
cnf(multiply_substitution1,axiom,
( equalish(multiply(X,W),multiply(Y,W))
| ~ equalish(X,Y) ),
file('theBenchmark.p',multiply_substitution1) ).
cnf(product_substitution1,axiom,
( product(Y,W,Z)
| ~ product(X,W,Z)
| ~ equalish(X,Y) ),
file('theBenchmark.p',product_substitution1) ).
cnf(product_substitution2,axiom,
( product(W,Y,Z)
| ~ product(W,X,Z)
| ~ equalish(X,Y) ),
file('theBenchmark.p',product_substitution2) ).
cnf(product_substitution3,axiom,
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('theBenchmark.p',product_substitution3) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('theBenchmark.p',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X),
file('theBenchmark.p',additive_identity2) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('theBenchmark.p',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('theBenchmark.p',closure_of_addition) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X),X,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(right_inverse,axiom,
sum(X,additive_inverse(X),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(associativity_of_addition1,axiom,
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('theBenchmark.p',associativity_of_addition1) ).
cnf(associativity_of_addition2,axiom,
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(commutativity_of_addition,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(associativity_of_multiplication1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('theBenchmark.p',associativity_of_multiplication1) ).
cnf(associativity_of_multiplication2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('theBenchmark.p',associativity_of_multiplication2) ).
cnf(distributivity1,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('theBenchmark.p',distributivity1) ).
cnf(distributivity2,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('theBenchmark.p',distributivity2) ).
cnf(distributivity3,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('theBenchmark.p',distributivity3) ).
cnf(distributivity4,axiom,
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('theBenchmark.p',distributivity4) ).
cnf(addition_is_well_defined,axiom,
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('theBenchmark.p',addition_is_well_defined) ).
cnf(multiplication_is_well_defined,axiom,
( equalish(U,V)
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('theBenchmark.p',multiplication_is_well_defined) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X,additive_identity),
file('theBenchmark.p',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X,additive_identity,additive_identity),
file('theBenchmark.p',multiplicative_identity2) ).
cnf(product_lemma1,axiom,
( product(A,additive_inverse(B),additive_inverse(C))
| ~ product(A,B,C) ),
file('theBenchmark.p',product_lemma1) ).
cnf(product_lemma2,axiom,
( product(additive_inverse(A),B,additive_inverse(C))
| ~ product(A,B,C) ),
file('theBenchmark.p',product_lemma2) ).
cnf(product_lemma3,axiom,
( product(additive_inverse(A),additive_inverse(B),C)
| ~ product(A,B,C) ),
file('theBenchmark.p',product_lemma3) ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('theBenchmark.p',b_plus_inverse_c) ).
cnf(a_times_b,hypothesis,
product(a,b,aPb),
file('theBenchmark.p',a_times_b) ).
cnf(a_times_c,hypothesis,
product(a,c,aPc),
file('theBenchmark.p',a_times_c) ).
cnf(aPb_plus_IaPc,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('theBenchmark.p',aPb_plus_IaPc) ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/25.40 % Computer : n019.cluster.edu
% 0.08/25.40 % Model : x86_64 x86_64
% 0.08/25.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/25.40 % Memory : 8046.5625MB
% 0.08/25.40 % OS : Linux 6.8.0-71-generic
% 0.08/25.40 % CPULimit : 300
% 0.08/25.40 % WCLimit : 300
% 0.08/25.40 % DateTime : Sat Sep 19 20:34:50 UTC 2026
% 0.08/25.40 % CPUTime :
% 120.11/145.46 % SZS status Unsatisfiable for theBenchmark
% 120.11/145.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------