%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:25:02 PM UTC 2026
% Result : Unsatisfiable 25.73s 3.72s
% Output : Proof 25.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 19
% Syntax : Number of formulae : 209 ( 189 unt; 0 def)
% Number of atoms : 257 ( 155 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 90 ( 42 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 262 ( 2 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
fof(f8_nnf,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t21,plain,
ifeq(subgroup_member(X1),true,ifeq(subgroup_member(X2),true,ifeq(product(X1,inverse(X2),X3),true,subgroup_member(X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t112,plain,
ifeq(subgroup_member(X1),true,ifeq(subgroup_member(X2),true,ifeq(product(X1,inverse(X2),X3),true,subgroup_member(X3),true),true),true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f0,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f0_nnf,plain,
! [X] : product(identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : product(identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t10,plain,
product(identity,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t43,plain,
product(identity,X1,X1) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t116,plain,
true = ifeq(subgroup_member(identity),true,ifeq(subgroup_member(X1),true,ifeq(true,true,subgroup_member(inverse(X1)),true),true),true),
inference(cp,[status(thm)],[t112,t43]) ).
cnf(f3,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f3_nnf,plain,
! [X] : product(X,inverse(X),identity),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : product(X,inverse(X),identity),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t12,plain,
product(X1,inverse(X1),identity) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t33,plain,
product(X1,inverse(X1),identity) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t113,plain,
true = ifeq(subgroup_member(X1),true,ifeq(subgroup_member(X1),true,ifeq(true,true,subgroup_member(identity),true),true),true),
inference(cp,[status(thm)],[t112,t33]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t7227,plain,
true = ifeq(subgroup_member(X1),true,ifeq(subgroup_member(X1),true,subgroup_member(identity),true),true),
inference(step,[status(thm)],[t113,t24]) ).
cnf(t282,plain,
ifeq(subgroup_member(X1),true,ifeq(subgroup_member(X1),true,subgroup_member(identity),true),true) = true,
inference(orient,[status(thm)],[t7227]) ).
cnf(f9,axiom,
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f9_nnf,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t18,plain,
or(subgroup_member(element_in_O2(X1,X2)),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t128,plain,
or(subgroup_member(element_in_O2(X1,X2)),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(f11,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).
fof(f11_nnf,plain,
~ subgroup_member(a),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ subgroup_member(a),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ subgroup_member(a),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t0,plain,
subgroup_member(a) = false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t129,plain,
subgroup_member(a) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t130,plain,
true = or(subgroup_member(element_in_O2(X1,a)),or(false,subgroup_member(X1))),
inference(cp,[status(thm)],[t128,t129]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t28,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t7179,plain,
true = or(subgroup_member(element_in_O2(X1,a)),subgroup_member(X1)),
inference(step,[status(thm)],[t130,t28]) ).
cnf(t148,plain,
or(subgroup_member(element_in_O2(X1,a)),subgroup_member(X1)) = true,
inference(orient,[status(thm)],[t7179]) ).
cnf(f13,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).
fof(f13_nnf,plain,
~ subgroup_member(d),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ subgroup_member(d),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t2,plain,
subgroup_member(d) = false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t138,plain,
subgroup_member(d) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t149,plain,
true = or(subgroup_member(element_in_O2(d,a)),false),
inference(cp,[status(thm)],[t148,t138]) ).
cnf(t4,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t27,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t7180,plain,
true = subgroup_member(element_in_O2(d,a)),
inference(step,[status(thm)],[t149,t27]) ).
cnf(t151,plain,
subgroup_member(element_in_O2(d,a)) = true,
inference(orient,[status(thm)],[t7180]) ).
cnf(t283,plain,
true = ifeq(true,true,ifeq(subgroup_member(element_in_O2(d,a)),true,subgroup_member(identity),true),true),
inference(cp,[status(thm)],[t282,t151]) ).
cnf(t7228,plain,
true = ifeq(subgroup_member(element_in_O2(d,a)),true,subgroup_member(identity),true),
inference(step,[status(thm)],[t283,t24]) ).
cnf(t7229,plain,
true = ifeq(true,true,subgroup_member(identity),true),
inference(step,[status(thm)],[t7228,t151]) ).
cnf(t7230,plain,
true = subgroup_member(identity),
inference(step,[status(thm)],[t7229,t24]) ).
cnf(t297,plain,
subgroup_member(identity) = true,
inference(orient,[status(thm)],[t7230]) ).
cnf(t7237,plain,
true = ifeq(true,true,ifeq(subgroup_member(X1),true,ifeq(true,true,subgroup_member(inverse(X1)),true),true),true),
inference(step,[status(thm)],[t116,t297]) ).
cnf(t7238,plain,
true = ifeq(subgroup_member(X1),true,ifeq(true,true,subgroup_member(inverse(X1)),true),true),
inference(step,[status(thm)],[t7237,t24]) ).
cnf(t7239,plain,
true = ifeq(subgroup_member(X1),true,subgroup_member(inverse(X1)),true),
inference(step,[status(thm)],[t7238,t24]) ).
cnf(t309,plain,
ifeq(subgroup_member(X1),true,subgroup_member(inverse(X1)),true) = true,
inference(orient,[status(thm)],[t7239]) ).
cnf(f12,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f12_nnf,plain,
subgroup_member(b),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
subgroup_member(b),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t1,plain,
subgroup_member(b) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t121,plain,
subgroup_member(b) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t315,plain,
true = ifeq(true,true,subgroup_member(inverse(b)),true),
inference(cp,[status(thm)],[t309,t121]) ).
cnf(t7240,plain,
true = subgroup_member(inverse(b)),
inference(step,[status(thm)],[t315,t24]) ).
cnf(t318,plain,
subgroup_member(inverse(b)) = true,
inference(orient,[status(thm)],[t7240]) ).
cnf(t320,plain,
true = ifeq(subgroup_member(X1),true,ifeq(true,true,ifeq(product(X1,inverse(inverse(b)),X2),true,subgroup_member(X2),true),true),true),
inference(cp,[status(thm)],[t112,t318]) ).
cnf(t7583,plain,
true = ifeq(subgroup_member(X1),true,ifeq(product(X1,inverse(inverse(b)),X2),true,subgroup_member(X2),true),true),
inference(step,[status(thm)],[t320,t24]) ).
cnf(f16,negated_conjecture,
inverse(inverse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
fof(f16_nnf,plain,
! [A] : inverse(inverse(A)) = A,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A] : inverse(inverse(A)) = A,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t3,plain,
inverse(inverse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t29,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t7584,plain,
true = ifeq(subgroup_member(X1),true,ifeq(product(X1,b,X2),true,subgroup_member(X2),true),true),
inference(step,[status(thm)],[t7583,t29]) ).
cnf(t7115,plain,
ifeq(subgroup_member(X1),true,ifeq(product(X1,b,X2),true,subgroup_member(X2),true),true) = true,
inference(orient,[status(thm)],[t7584]) ).
cnf(f6,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f6_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t23,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X3,X4,X6),true,product(X1,X5,X6),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t52,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X3,X4,X6),true,product(X1,X5,X6),true),true),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t55,plain,
true = ifeq(true,true,ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true),true),
inference(cp,[status(thm)],[t52,t33]) ).
cnf(t7266,plain,
true = ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true),
inference(step,[status(thm)],[t55,t24]) ).
cnf(t716,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t7266]) ).
cnf(t725,plain,
true = ifeq(product(inverse(X1),X2,X3),true,ifeq(true,true,product(X1,X3,X2),true),true),
inference(cp,[status(thm)],[t716,t43]) ).
cnf(t7272,plain,
true = ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true),
inference(step,[status(thm)],[t725,t24]) ).
cnf(t792,plain,
ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t7272]) ).
cnf(f4,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
fof(f4_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t17,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t30,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t793,plain,
true = ifeq(true,true,product(X1,multiply(inverse(X1),X2),X2),true),
inference(cp,[status(thm)],[t792,t30]) ).
cnf(t7273,plain,
true = product(X1,multiply(inverse(X1),X2),X2),
inference(step,[status(thm)],[t793,t24]) ).
cnf(t805,plain,
product(X1,multiply(inverse(X1),X2),X2) = true,
inference(orient,[status(thm)],[t7273]) ).
cnf(t806,plain,
true = product(inverse(X1),multiply(X1,X2),X2),
inference(cp,[status(thm)],[t805,t29]) ).
cnf(t954,plain,
product(inverse(X1),multiply(X1,X2),X2) = true,
inference(orient,[status(thm)],[t806]) ).
cnf(f5,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f5_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t20,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t25,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t20]) ).
cnf(t32,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,ifeq(true,true,X3,multiply(X1,X2)),multiply(X1,X2)),
inference(cp,[status(thm)],[t25,t30]) ).
cnf(t7226,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)),
inference(step,[status(thm)],[t32,t24]) ).
cnf(t281,plain,
ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t7226]) ).
cnf(f14,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f14_nnf,plain,
product(b,inverse(a),c),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(t13,plain,
product(b,inverse(a),c) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t49,plain,
product(b,inverse(a),c) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t56,plain,
true = ifeq(true,true,ifeq(product(inverse(a),X1,X2),true,ifeq(product(c,X1,X3),true,product(b,X2,X3),true),true),true),
inference(cp,[status(thm)],[t52,t49]) ).
cnf(t7305,plain,
true = ifeq(product(inverse(a),X1,X2),true,ifeq(product(c,X1,X3),true,product(b,X2,X3),true),true),
inference(step,[status(thm)],[t56,t24]) ).
cnf(t991,plain,
ifeq(product(inverse(a),X1,X2),true,ifeq(product(c,X1,X3),true,product(b,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t7305]) ).
cnf(f2,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f2_nnf,plain,
! [X] : product(inverse(X),X,identity),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : product(inverse(X),X,identity),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t14,plain,
product(inverse(X1),X1,identity) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t40,plain,
product(inverse(X1),X1,identity) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t993,plain,
true = ifeq(true,true,ifeq(product(c,a,X1),true,product(b,identity,X1),true),true),
inference(cp,[status(thm)],[t991,t40]) ).
cnf(t7317,plain,
true = ifeq(product(c,a,X1),true,product(b,identity,X1),true),
inference(step,[status(thm)],[t993,t24]) ).
cnf(t1135,plain,
ifeq(product(c,a,X1),true,product(b,identity,X1),true) = true,
inference(orient,[status(thm)],[t7317]) ).
cnf(t1136,plain,
true = ifeq(true,true,product(b,identity,multiply(c,a)),true),
inference(cp,[status(thm)],[t1135,t30]) ).
cnf(t7318,plain,
true = product(b,identity,multiply(c,a)),
inference(step,[status(thm)],[t1136,t24]) ).
cnf(t1142,plain,
product(b,identity,multiply(c,a)) = true,
inference(orient,[status(thm)],[t7318]) ).
cnf(t1145,plain,
multiply(b,identity) = ifeq(true,true,multiply(c,a),multiply(b,identity)),
inference(cp,[status(thm)],[t281,t1142]) ).
cnf(f1,axiom,
product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f1_nnf,plain,
! [X] : product(X,identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : product(X,identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(X0,identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t8,plain,
product(X1,identity,X1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t37,plain,
product(X1,identity,X1) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t38,plain,
X1 = ifeq(true,true,ifeq(product(X2,identity,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t25,t37]) ).
cnf(t7187,plain,
X1 = ifeq(product(X2,identity,X1),true,X2,X1),
inference(step,[status(thm)],[t38,t24]) ).
cnf(t172,plain,
ifeq(product(X1,identity,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t7187]) ).
cnf(t173,plain,
multiply(X1,identity) = ifeq(true,true,X1,multiply(X1,identity)),
inference(cp,[status(thm)],[t172,t30]) ).
cnf(t7189,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t173,t24]) ).
cnf(t181,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t7189]) ).
cnf(t7319,plain,
b = ifeq(true,true,multiply(c,a),multiply(b,identity)),
inference(step,[status(thm)],[t1145,t181]) ).
cnf(t7320,plain,
b = multiply(c,a),
inference(step,[status(thm)],[t7319,t24]) ).
cnf(t1167,plain,
multiply(c,a) = b,
inference(orient,[status(thm)],[t7320]) ).
cnf(t1168,plain,
true = product(inverse(c),b,a),
inference(cp,[status(thm)],[t954,t1167]) ).
cnf(t1228,plain,
product(inverse(c),b,a) = true,
inference(orient,[status(thm)],[t1168]) ).
cnf(t7127,plain,
true = ifeq(subgroup_member(inverse(c)),true,ifeq(true,true,subgroup_member(a),true),true),
inference(cp,[status(thm)],[t7115,t1228]) ).
cnf(t131,plain,
true = or(subgroup_member(element_in_O2(a,X1)),or(subgroup_member(X1),false)),
inference(cp,[status(thm)],[t128,t129]) ).
cnf(t7182,plain,
true = or(subgroup_member(element_in_O2(a,X1)),subgroup_member(X1)),
inference(step,[status(thm)],[t131,t27]) ).
cnf(t159,plain,
or(subgroup_member(element_in_O2(a,X1)),subgroup_member(X1)) = true,
inference(orient,[status(thm)],[t7182]) ).
cnf(t160,plain,
true = or(subgroup_member(element_in_O2(a,d)),false),
inference(cp,[status(thm)],[t159,t138]) ).
cnf(t7183,plain,
true = subgroup_member(element_in_O2(a,d)),
inference(step,[status(thm)],[t160,t27]) ).
cnf(t161,plain,
subgroup_member(element_in_O2(a,d)) = true,
inference(orient,[status(thm)],[t7183]) ).
cnf(t313,plain,
true = ifeq(true,true,subgroup_member(inverse(element_in_O2(a,d))),true),
inference(cp,[status(thm)],[t309,t161]) ).
cnf(t7244,plain,
true = subgroup_member(inverse(element_in_O2(a,d))),
inference(step,[status(thm)],[t313,t24]) ).
cnf(t334,plain,
subgroup_member(inverse(element_in_O2(a,d))) = true,
inference(orient,[status(thm)],[t7244]) ).
cnf(t808,plain,
multiply(X1,multiply(inverse(X1),X2)) = ifeq(true,true,X2,multiply(X1,multiply(inverse(X1),X2))),
inference(cp,[status(thm)],[t281,t805]) ).
cnf(t7274,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t808,t24]) ).
cnf(t828,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t7274]) ).
cnf(t829,plain,
X1 = multiply(inverse(X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t828,t29]) ).
cnf(t834,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t829]) ).
cnf(t31,plain,
X1 = ifeq(true,true,ifeq(product(X2,X3,X1),true,multiply(X2,X3),X1),X1),
inference(cp,[status(thm)],[t25,t30]) ).
cnf(t7213,plain,
X1 = ifeq(product(X2,X3,X1),true,multiply(X2,X3),X1),
inference(step,[status(thm)],[t31,t24]) ).
cnf(t260,plain,
ifeq(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(orient,[status(thm)],[t7213]) ).
cnf(f10,axiom,
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f10_nnf,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t19,plain,
or(product(X1,element_in_O2(X1,X2),X2),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t127,plain,
or(product(X1,element_in_O2(X1,X2),X2),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t133,plain,
true = or(product(a,element_in_O2(a,X1),X1),or(subgroup_member(X1),false)),
inference(cp,[status(thm)],[t127,t129]) ).
cnf(t7208,plain,
true = or(product(a,element_in_O2(a,X1),X1),subgroup_member(X1)),
inference(step,[status(thm)],[t133,t27]) ).
cnf(t233,plain,
or(product(a,element_in_O2(a,X1),X1),subgroup_member(X1)) = true,
inference(orient,[status(thm)],[t7208]) ).
cnf(t234,plain,
true = or(product(a,element_in_O2(a,d),d),false),
inference(cp,[status(thm)],[t233,t138]) ).
cnf(t7209,plain,
true = product(a,element_in_O2(a,d),d),
inference(step,[status(thm)],[t234,t27]) ).
cnf(t235,plain,
product(a,element_in_O2(a,d),d) = true,
inference(orient,[status(thm)],[t7209]) ).
cnf(t264,plain,
d = ifeq(true,true,multiply(a,element_in_O2(a,d)),d),
inference(cp,[status(thm)],[t260,t235]) ).
cnf(t7217,plain,
d = multiply(a,element_in_O2(a,d)),
inference(step,[status(thm)],[t264,t24]) ).
cnf(t271,plain,
multiply(a,element_in_O2(a,d)) = d,
inference(orient,[status(thm)],[t7217]) ).
cnf(t840,plain,
element_in_O2(a,d) = multiply(inverse(a),d),
inference(cp,[status(thm)],[t834,t271]) ).
cnf(f15,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f15_nnf,plain,
product(a,c,d),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
product(a,c,d),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t9,plain,
product(a,c,d) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t46,plain,
product(a,c,d) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t47,plain,
X1 = ifeq(true,true,ifeq(product(a,c,X1),true,d,X1),X1),
inference(cp,[status(thm)],[t25,t46]) ).
cnf(t7194,plain,
X1 = ifeq(product(a,c,X1),true,d,X1),
inference(step,[status(thm)],[t47,t24]) ).
cnf(t189,plain,
ifeq(product(a,c,X1),true,d,X1) = X1,
inference(orient,[status(thm)],[t7194]) ).
cnf(t190,plain,
multiply(a,c) = ifeq(true,true,d,multiply(a,c)),
inference(cp,[status(thm)],[t189,t30]) ).
cnf(t7195,plain,
multiply(a,c) = d,
inference(step,[status(thm)],[t190,t24]) ).
cnf(t191,plain,
multiply(a,c) = d,
inference(orient,[status(thm)],[t7195]) ).
cnf(t838,plain,
c = multiply(inverse(a),d),
inference(cp,[status(thm)],[t834,t191]) ).
cnf(t848,plain,
multiply(inverse(a),d) = c,
inference(orient,[status(thm)],[t838]) ).
cnf(t7277,plain,
element_in_O2(a,d) = c,
inference(step,[status(thm)],[t840,t848]) ).
cnf(t866,plain,
element_in_O2(a,d) = c,
inference(orient,[status(thm)],[t7277]) ).
cnf(t7291,plain,
subgroup_member(inverse(c)) = true,
inference(step,[status(thm)],[t334,t866]) ).
cnf(t883,plain,
subgroup_member(inverse(c)) = true,
inference(rw,[status(thm)],[t7291]) ).
cnf(t908,plain,
subgroup_member(inverse(c)) = true,
inference(orient,[status(thm)],[t883]) ).
cnf(t7585,plain,
true = ifeq(true,true,ifeq(true,true,subgroup_member(a),true),true),
inference(step,[status(thm)],[t7127,t908]) ).
cnf(t7586,plain,
true = ifeq(true,true,subgroup_member(a),true),
inference(step,[status(thm)],[t7585,t24]) ).
cnf(t7587,plain,
true = subgroup_member(a),
inference(step,[status(thm)],[t7586,t24]) ).
cnf(t7588,plain,
true = false,
inference(step,[status(thm)],[t7587,t129]) ).
cnf(t7138,plain,
false = true,
inference(orient,[status(thm)],[t7588]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c11,c13]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t7138]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:24:38 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.73/3.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.73/3.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------