%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 15.98s 2.47s
% Output : Proof 15.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 20
% Syntax : Number of formulae : 190 ( 162 unt; 0 def)
% Number of atoms : 250 ( 132 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 114 ( 54 ~; 60 |; 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 : 270 ( 2 sgn 58 !; 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(t25,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(t150,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)],[t25]) ).
cnf(f10,axiom,
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f10_nnf,plain,
! [A] :
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] :
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t19,plain,
ifeq(subgroup_member(X1),true,subgroup_member(inverse(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t157,plain,
ifeq(subgroup_member(X1),true,subgroup_member(inverse(X1)),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(f16,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f16_nnf,plain,
subgroup_member(b),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
subgroup_member(b),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t1,plain,
subgroup_member(b) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t166,plain,
subgroup_member(b) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t167,plain,
true = ifeq(true,true,subgroup_member(inverse(b)),true),
inference(cp,[status(thm)],[t157,t166]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t3246,plain,
true = subgroup_member(inverse(b)),
inference(step,[status(thm)],[t167,t28]) ).
cnf(t199,plain,
subgroup_member(inverse(b)) = true,
inference(orient,[status(thm)],[t3246]) ).
cnf(t201,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)],[t150,t199]) ).
cnf(t3335,plain,
true = ifeq(subgroup_member(X1),true,ifeq(product(X1,inverse(inverse(b)),X2),true,subgroup_member(X2),true),true),
inference(step,[status(thm)],[t201,t28]) ).
cnf(f20,negated_conjecture,
inverse(inverse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
fof(f20_nnf,plain,
! [A] : inverse(inverse(A)) = A,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A] : inverse(inverse(A)) = A,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t4,plain,
inverse(inverse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t37,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t3336,plain,
true = ifeq(subgroup_member(X1),true,ifeq(product(X1,b,X2),true,subgroup_member(X2),true),true),
inference(step,[status(thm)],[t3335,t37]) ).
cnf(t528,plain,
ifeq(subgroup_member(X1),true,ifeq(product(X1,b,X2),true,subgroup_member(X2),true),true) = true,
inference(orient,[status(thm)],[t3336]) ).
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(t18,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t38,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t539,plain,
true = ifeq(subgroup_member(X1),true,ifeq(true,true,subgroup_member(multiply(X1,b)),true),true),
inference(cp,[status(thm)],[t528,t38]) ).
cnf(t3344,plain,
true = ifeq(subgroup_member(X1),true,subgroup_member(multiply(X1,b)),true),
inference(step,[status(thm)],[t539,t28]) ).
cnf(t638,plain,
ifeq(subgroup_member(X1),true,subgroup_member(multiply(X1,b)),true) = true,
inference(orient,[status(thm)],[t3344]) ).
cnf(f11,axiom,
( D = B
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f11_nnf,plain,
! [A,B,C,D] :
( D = B
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,C,D] :
( D = B
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( X3 = X1
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t23,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X3),true,X4,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t31,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X3),true,X4,X2),X2) = X2,
inference(orient,[status(thm)],[t23]) ).
cnf(t43,plain,
X1 = ifeq(true,true,ifeq(product(X2,X3,multiply(X2,X1)),true,X3,X1),X1),
inference(cp,[status(thm)],[t31,t38]) ).
cnf(t3316,plain,
X1 = ifeq(product(X2,X3,multiply(X2,X1)),true,X3,X1),
inference(step,[status(thm)],[t43,t28]) ).
cnf(t484,plain,
ifeq(product(X1,X2,multiply(X1,X3)),true,X2,X3) = X3,
inference(orient,[status(thm)],[t3316]) ).
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(t22,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t29,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t22]) ).
cnf(t40,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,ifeq(true,true,X3,multiply(X1,X2)),multiply(X1,X2)),
inference(cp,[status(thm)],[t29,t38]) ).
cnf(t3324,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)),
inference(step,[status(thm)],[t40,t28]) ).
cnf(t512,plain,
ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t3324]) ).
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(t27,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(t88,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)],[t27]) ).
cnf(f18,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f18_nnf,plain,
product(b,inverse(a),c),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t14,plain,
product(b,inverse(a),c) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t81,plain,
product(b,inverse(a),c) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t92,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)],[t88,t81]) ).
cnf(t3428,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)],[t92,t28]) ).
cnf(t2299,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)],[t3428]) ).
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(t15,plain,
product(inverse(X1),X1,identity) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t60,plain,
product(inverse(X1),X1,identity) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t2300,plain,
true = ifeq(true,true,ifeq(product(c,a,X1),true,product(b,identity,X1),true),true),
inference(cp,[status(thm)],[t2299,t60]) ).
cnf(t3429,plain,
true = ifeq(product(c,a,X1),true,product(b,identity,X1),true),
inference(step,[status(thm)],[t2300,t28]) ).
cnf(t2313,plain,
ifeq(product(c,a,X1),true,product(b,identity,X1),true) = true,
inference(orient,[status(thm)],[t3429]) ).
cnf(t2314,plain,
true = ifeq(true,true,product(b,identity,multiply(c,a)),true),
inference(cp,[status(thm)],[t2313,t38]) ).
cnf(t3430,plain,
true = product(b,identity,multiply(c,a)),
inference(step,[status(thm)],[t2314,t28]) ).
cnf(t2320,plain,
product(b,identity,multiply(c,a)) = true,
inference(orient,[status(thm)],[t3430]) ).
cnf(t2322,plain,
multiply(b,identity) = ifeq(true,true,multiply(c,a),multiply(b,identity)),
inference(cp,[status(thm)],[t512,t2320]) ).
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(t9,plain,
product(X1,identity,X1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t53,plain,
product(X1,identity,X1) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t54,plain,
X1 = ifeq(true,true,ifeq(product(X2,identity,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t29,t53]) ).
cnf(t3259,plain,
X1 = ifeq(product(X2,identity,X1),true,X2,X1),
inference(step,[status(thm)],[t54,t28]) ).
cnf(t250,plain,
ifeq(product(X1,identity,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t3259]) ).
cnf(t251,plain,
multiply(X1,identity) = ifeq(true,true,X1,multiply(X1,identity)),
inference(cp,[status(thm)],[t250,t38]) ).
cnf(t3261,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t251,t28]) ).
cnf(t259,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t3261]) ).
cnf(t3431,plain,
b = ifeq(true,true,multiply(c,a),multiply(b,identity)),
inference(step,[status(thm)],[t2322,t259]) ).
cnf(t3432,plain,
b = multiply(c,a),
inference(step,[status(thm)],[t3431,t28]) ).
cnf(t2348,plain,
multiply(c,a) = b,
inference(orient,[status(thm)],[t3432]) ).
cnf(t2356,plain,
a = ifeq(product(c,X1,b),true,X1,a),
inference(cp,[status(thm)],[t484,t2348]) ).
cnf(t2392,plain,
ifeq(product(c,X1,b),true,X1,a) = a,
inference(orient,[status(thm)],[t2356]) ).
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(t13,plain,
product(X1,inverse(X1),identity) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t45,plain,
product(X1,inverse(X1),identity) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t91,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)],[t88,t45]) ).
cnf(t3416,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)],[t91,t28]) ).
cnf(t1860,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)],[t3416]) ).
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(t11,plain,
product(identity,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t67,plain,
product(identity,X1,X1) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t1868,plain,
true = ifeq(product(inverse(X1),X2,X3),true,ifeq(true,true,product(X1,X3,X2),true),true),
inference(cp,[status(thm)],[t1860,t67]) ).
cnf(t3482,plain,
true = ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true),
inference(step,[status(thm)],[t1868,t28]) ).
cnf(t3068,plain,
ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t3482]) ).
cnf(t3069,plain,
true = ifeq(true,true,product(X1,multiply(inverse(X1),X2),X2),true),
inference(cp,[status(thm)],[t3068,t38]) ).
cnf(t3483,plain,
true = product(X1,multiply(inverse(X1),X2),X2),
inference(step,[status(thm)],[t3069,t28]) ).
cnf(t3080,plain,
product(X1,multiply(inverse(X1),X2),X2) = true,
inference(orient,[status(thm)],[t3483]) ).
cnf(t3084,plain,
a = ifeq(true,true,multiply(inverse(c),b),a),
inference(cp,[status(thm)],[t2392,t3080]) ).
cnf(t3485,plain,
a = multiply(inverse(c),b),
inference(step,[status(thm)],[t3084,t28]) ).
cnf(t3163,plain,
multiply(inverse(c),b) = a,
inference(orient,[status(thm)],[t3485]) ).
cnf(t3168,plain,
true = ifeq(subgroup_member(inverse(c)),true,subgroup_member(a),true),
inference(cp,[status(thm)],[t638,t3163]) ).
cnf(f13,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(f13_nnf,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t20,plain,
or(subgroup_member(element_in_O2(X1,X2)),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t174,plain,
or(subgroup_member(element_in_O2(X1,X2)),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f15,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).
fof(f15_nnf,plain,
~ subgroup_member(a),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ subgroup_member(a),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ subgroup_member(a),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t0,plain,
subgroup_member(a) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t175,plain,
subgroup_member(a) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t177,plain,
true = or(subgroup_member(element_in_O2(a,X1)),or(subgroup_member(X1),false)),
inference(cp,[status(thm)],[t174,t175]) ).
cnf(t5,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t35,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t3252,plain,
true = or(subgroup_member(element_in_O2(a,X1)),subgroup_member(X1)),
inference(step,[status(thm)],[t177,t35]) ).
cnf(t225,plain,
or(subgroup_member(element_in_O2(a,X1)),subgroup_member(X1)) = true,
inference(orient,[status(thm)],[t3252]) ).
cnf(f17,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).
fof(f17_nnf,plain,
~ subgroup_member(d),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
~ subgroup_member(d),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t2,plain,
subgroup_member(d) = false,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t185,plain,
subgroup_member(d) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t226,plain,
true = or(subgroup_member(element_in_O2(a,d)),false),
inference(cp,[status(thm)],[t225,t185]) ).
cnf(t3253,plain,
true = subgroup_member(element_in_O2(a,d)),
inference(step,[status(thm)],[t226,t35]) ).
cnf(t227,plain,
subgroup_member(element_in_O2(a,d)) = true,
inference(orient,[status(thm)],[t3253]) ).
cnf(t228,plain,
true = ifeq(true,true,subgroup_member(inverse(element_in_O2(a,d))),true),
inference(cp,[status(thm)],[t157,t227]) ).
cnf(t3254,plain,
true = subgroup_member(inverse(element_in_O2(a,d))),
inference(step,[status(thm)],[t228,t28]) ).
cnf(t232,plain,
subgroup_member(inverse(element_in_O2(a,d))) = true,
inference(orient,[status(thm)],[t3254]) ).
cnf(f19,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f19_nnf,plain,
product(a,c,d),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
product(a,c,d),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t10,plain,
product(a,c,d) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t74,plain,
product(a,c,d) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t80,plain,
X1 = ifeq(product(a,X1,d),true,ifeq(true,true,c,X1),X1),
inference(cp,[status(thm)],[t31,t74]) ).
cnf(t3276,plain,
X1 = ifeq(product(a,X1,d),true,c,X1),
inference(step,[status(thm)],[t80,t28]) ).
cnf(t290,plain,
ifeq(product(a,X1,d),true,c,X1) = X1,
inference(orient,[status(thm)],[t3276]) ).
cnf(f14,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(f14_nnf,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t21,plain,
or(product(X1,element_in_O2(X1,X2),X2),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t173,plain,
or(product(X1,element_in_O2(X1,X2),X2),or(subgroup_member(X2),subgroup_member(X1))) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t179,plain,
true = or(product(a,element_in_O2(a,X1),X1),or(subgroup_member(X1),false)),
inference(cp,[status(thm)],[t173,t175]) ).
cnf(t3298,plain,
true = or(product(a,element_in_O2(a,X1),X1),subgroup_member(X1)),
inference(step,[status(thm)],[t179,t35]) ).
cnf(t392,plain,
or(product(a,element_in_O2(a,X1),X1),subgroup_member(X1)) = true,
inference(orient,[status(thm)],[t3298]) ).
cnf(t393,plain,
true = or(product(a,element_in_O2(a,d),d),false),
inference(cp,[status(thm)],[t392,t185]) ).
cnf(t3299,plain,
true = product(a,element_in_O2(a,d),d),
inference(step,[status(thm)],[t393,t35]) ).
cnf(t394,plain,
product(a,element_in_O2(a,d),d) = true,
inference(orient,[status(thm)],[t3299]) ).
cnf(t395,plain,
element_in_O2(a,d) = ifeq(true,true,c,element_in_O2(a,d)),
inference(cp,[status(thm)],[t290,t394]) ).
cnf(t3300,plain,
element_in_O2(a,d) = c,
inference(step,[status(thm)],[t395,t28]) ).
cnf(t411,plain,
element_in_O2(a,d) = c,
inference(orient,[status(thm)],[t3300]) ).
cnf(t3302,plain,
subgroup_member(inverse(c)) = true,
inference(step,[status(thm)],[t232,t411]) ).
cnf(t416,plain,
subgroup_member(inverse(c)) = true,
inference(rw,[status(thm)],[t3302]) ).
cnf(t423,plain,
subgroup_member(inverse(c)) = true,
inference(orient,[status(thm)],[t416]) ).
cnf(t3529,plain,
true = ifeq(true,true,subgroup_member(a),true),
inference(step,[status(thm)],[t3168,t423]) ).
cnf(t3530,plain,
true = subgroup_member(a),
inference(step,[status(thm)],[t3529,t28]) ).
cnf(t3531,plain,
true = false,
inference(step,[status(thm)],[t3530,t175]) ).
cnf(t3208,plain,
false = true,
inference(orient,[status(thm)],[t3531]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c15,c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3208]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:26:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.98/2.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.98/2.47 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------