%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 01:25:39 PM UTC 2026
% Result : Theorem 239.15s 33.84s
% Output : Proof 239.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 104 ( 80 unt; 0 def)
% Number of atoms : 156 ( 86 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 91 ( 39 ~; 34 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 93 ( 2 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
fof(f7_neg,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
~ left_zero(h,phi(f_left_zero)),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
~ left_zero(h,phi(f_left_zero)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c11,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t6,plain,
left_zero(h,phi(f_left_zero)) = false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t588,plain,
left_zero(h,phi(f_left_zero)) = false,
inference(orient,[status(thm)],[t6]) ).
fof(f5,axiom,
! [G,X] :
( left_zero(G,X)
<=> ( ! [Y] :
( group_member(Y,G)
=> multiply(G,X,Y) = X )
& group_member(X,G) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
fof(f5_nnf,plain,
! [G,X] :
( ( ? [Y] :
( multiply(G,X,Y) != X
& group_member(Y,G) )
| ~ group_member(X,G)
| left_zero(G,X) )
& ( ( ! [Y] :
( multiply(G,X,Y) = X
| ~ group_member(Y,G) )
& group_member(X,G) )
| ~ left_zero(G,X) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [G,X,Y] :
( ( ( multiply(G,X,sk1(G,X)) != X
& group_member(sk1(G,X),G) )
| ~ group_member(X,G)
| left_zero(G,X) )
& ( ( ( multiply(G,X,Y) = X
| ~ group_member(Y,G) )
& group_member(X,G) )
| ~ left_zero(G,X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f5_nnf]) ).
cnf(c9,plain,
( multiply(X0,X1,sk1(X0,X1)) != X1
| ~ group_member(X1,X0)
| left_zero(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t156,plain,
ifeq(group_member(X1,X2),true,ifeq(multiply(X2,X1,sk1(X2,X1)),X1,left_zero(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t555,plain,
ifeq(group_member(X1,X2),true,ifeq(multiply(X2,X1,sk1(X2,X1)),X1,left_zero(X2,X1),true),true) = true,
inference(orient,[status(thm)],[t156]) ).
fof(f3,axiom,
! [X,Y] :
( ( group_member(Y,f)
& group_member(X,f) )
=> multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f3_nnf,plain,
! [X,Y] :
( multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y))
| ~ group_member(Y,f)
| ~ group_member(X,f) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y))
| ~ group_member(Y,f)
| ~ group_member(X,f) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t254,plain,
ifeq(group_member(X1,f),true,ifeq(group_member(X2,f),true,multiply(h,phi(X1),phi(X2)),phi(multiply(f,X1,X2))),phi(multiply(f,X1,X2))) = phi(multiply(f,X1,X2)),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t329,plain,
ifeq(group_member(X1,f),true,ifeq(group_member(X2,f),true,multiply(h,phi(X1),phi(X2)),phi(multiply(f,X1,X2))),phi(multiply(f,X1,X2))) = phi(multiply(f,X1,X2)),
inference(orient,[status(thm)],[t254]) ).
cnf(c7,plain,
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t141,plain,
ifeq(left_zero(X1,X2),true,ifeq(group_member(X3,X1),true,multiply(X1,X2,X3),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t260,plain,
ifeq(left_zero(X1,X2),true,ifeq(group_member(X3,X1),true,multiply(X1,X2,X3),X2),X2) = X2,
inference(orient,[status(thm)],[t141]) ).
fof(f6,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
fof(f6_nnf,plain,
left_zero(f,f_left_zero),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c10,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t0,plain,
left_zero(f,f_left_zero) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t545,plain,
left_zero(f,f_left_zero) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t546,plain,
f_left_zero = ifeq(true,true,ifeq(group_member(X1,f),true,multiply(f,f_left_zero,X1),f_left_zero),f_left_zero),
inference(cp,[status(thm)],[t260,t545]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t675,plain,
f_left_zero = ifeq(group_member(X1,f),true,multiply(f,f_left_zero,X1),f_left_zero),
inference(step,[status(thm)],[t546,t258]) ).
cnf(t625,plain,
ifeq(group_member(X1,f),true,multiply(f,f_left_zero,X1),f_left_zero) = f_left_zero,
inference(orient,[status(thm)],[t675]) ).
fof(f4,axiom,
! [X] :
( group_member(X,h)
=> ? [Y] :
( phi(Y) = X
& group_member(Y,f) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f4_nnf,plain,
! [X] :
( ? [Y] :
( phi(Y) = X
& group_member(Y,f) )
| ~ group_member(X,h) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( ( phi(sk0(X)) = X
& group_member(sk0(X),f) )
| ~ group_member(X,h) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c4,plain,
( group_member(sk0(X0),f)
| ~ group_member(X0,h) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t44,plain,
ifeq(group_member(X1,h),true,group_member(sk0(X1),f),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t581,plain,
ifeq(group_member(X1,h),true,group_member(sk0(X1),f),true) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(c8,plain,
( group_member(sk1(X0,X1),X0)
| ~ group_member(X1,X0)
| left_zero(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t133,plain,
ifeq(group_member(X1,X2),true,or(left_zero(X2,X1),group_member(sk1(X2,X1),X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t554,plain,
ifeq(group_member(X1,X2),true,or(left_zero(X2,X1),group_member(sk1(X2,X1),X2)),true) = true,
inference(orient,[status(thm)],[t133]) ).
cnf(t592,plain,
true = ifeq(group_member(phi(f_left_zero),h),true,or(false,group_member(sk1(h,phi(f_left_zero)),h)),true),
inference(cp,[status(thm)],[t554,t588]) ).
cnf(c6,plain,
( group_member(X1,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi6,axiom,
ifeq(left_zero(X0,X1),true,group_member(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(hi10,axiom,
left_zero(f,f_left_zero) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h0,plain,
group_member(f_left_zero,f) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi10]) ).
fof(f2,axiom,
! [X] :
( group_member(X,f)
=> group_member(phi(X),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f2_nnf,plain,
! [X] :
( group_member(phi(X),h)
| ~ group_member(X,f) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( group_member(phi(X),h)
| ~ group_member(X,f) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(group_member(X0,f),true,group_member(phi(X0),h),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t5,plain,
group_member(phi(f_left_zero),h) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
cnf(t505,plain,
group_member(phi(f_left_zero),h) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t669,plain,
true = ifeq(true,true,or(false,group_member(sk1(h,phi(f_left_zero)),h)),true),
inference(step,[status(thm)],[t592,t505]) ).
cnf(t670,plain,
true = or(false,group_member(sk1(h,phi(f_left_zero)),h)),
inference(step,[status(thm)],[t669,t258]) ).
cnf(t3,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t671,plain,
true = group_member(sk1(h,phi(f_left_zero)),h),
inference(step,[status(thm)],[t670,t257]) ).
cnf(t595,plain,
group_member(sk1(h,phi(f_left_zero)),h) = true,
inference(orient,[status(thm)],[t671]) ).
cnf(t598,plain,
true = ifeq(true,true,group_member(sk0(sk1(h,phi(f_left_zero))),f),true),
inference(cp,[status(thm)],[t581,t595]) ).
cnf(t672,plain,
true = group_member(sk0(sk1(h,phi(f_left_zero))),f),
inference(step,[status(thm)],[t598,t258]) ).
cnf(t607,plain,
group_member(sk0(sk1(h,phi(f_left_zero))),f) = true,
inference(orient,[status(thm)],[t672]) ).
cnf(t626,plain,
f_left_zero = ifeq(true,true,multiply(f,f_left_zero,sk0(sk1(h,phi(f_left_zero)))),f_left_zero),
inference(cp,[status(thm)],[t625,t607]) ).
cnf(t676,plain,
f_left_zero = multiply(f,f_left_zero,sk0(sk1(h,phi(f_left_zero)))),
inference(step,[status(thm)],[t626,t258]) ).
cnf(t629,plain,
multiply(f,f_left_zero,sk0(sk1(h,phi(f_left_zero)))) = f_left_zero,
inference(orient,[status(thm)],[t676]) ).
cnf(t630,plain,
phi(multiply(f,f_left_zero,sk0(sk1(h,phi(f_left_zero))))) = ifeq(group_member(f_left_zero,f),true,ifeq(group_member(sk0(sk1(h,phi(f_left_zero))),f),true,multiply(h,phi(f_left_zero),phi(sk0(sk1(h,phi(f_left_zero))))),phi(f_left_zero)),phi(multiply(f,f_left_zero,sk0(sk1(h,phi(f_left_zero)))))),
inference(cp,[status(thm)],[t329,t629]) ).
cnf(t677,plain,
phi(f_left_zero) = ifeq(group_member(f_left_zero,f),true,ifeq(group_member(sk0(sk1(h,phi(f_left_zero))),f),true,multiply(h,phi(f_left_zero),phi(sk0(sk1(h,phi(f_left_zero))))),phi(f_left_zero)),phi(multiply(f,f_left_zero,sk0(sk1(h,phi(f_left_zero)))))),
inference(step,[status(thm)],[t630,t629]) ).
cnf(h4,plain,
group_member(phi(f_left_zero),h) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
cnf(hi4,axiom,
ifeq(group_member(X0,h),true,group_member(sk0(X0),f),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h9,plain,
group_member(sk0(phi(f_left_zero)),f) = true,
inference(hyper_resolution,[status(thm)],[hi4,h4]) ).
fof(f0,axiom,
! [G,X,Y] :
( ( group_member(Y,G)
& group_member(X,G) )
=> group_member(multiply(G,X,Y),G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function) ).
fof(f0_nnf,plain,
! [G,X,Y] :
( group_member(multiply(G,X,Y),G)
| ~ group_member(Y,G)
| ~ group_member(X,G) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,G,Y] :
( group_member(multiply(G,X,Y),G)
| ~ group_member(Y,G)
| ~ group_member(X,G) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( group_member(multiply(X0,X1,X2),X0)
| ~ group_member(X2,X0)
| ~ group_member(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(group_member(X0,X1),true,ifeq(group_member(X2,X1),true,group_member(multiply(X1,X0,X2),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t14,plain,
group_member(multiply(f,f_left_zero,sk0(phi(f_left_zero))),f) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h9]) ).
cnf(hi7,axiom,
ifeq(left_zero(X0,X1),true,ifeq(group_member(X2,X0),true,multiply(X0,X1,X2),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t11,plain,
multiply(f,f_left_zero,sk0(phi(f_left_zero))) = f_left_zero,
inference(hyper_resolution,[status(thm)],[hi7,hi10,h9]) ).
cnf(t406,plain,
multiply(f,f_left_zero,sk0(phi(f_left_zero))) = f_left_zero,
inference(orient,[status(thm)],[t11]) ).
cnf(t665,plain,
group_member(f_left_zero,f) = true,
inference(step,[status(thm)],[t14,t406]) ).
cnf(t517,plain,
group_member(f_left_zero,f) = true,
inference(orient,[status(thm)],[t665]) ).
cnf(t678,plain,
phi(f_left_zero) = ifeq(true,true,ifeq(group_member(sk0(sk1(h,phi(f_left_zero))),f),true,multiply(h,phi(f_left_zero),phi(sk0(sk1(h,phi(f_left_zero))))),phi(f_left_zero)),phi(multiply(f,f_left_zero,sk0(sk1(h,phi(f_left_zero)))))),
inference(step,[status(thm)],[t677,t517]) ).
cnf(t679,plain,
phi(f_left_zero) = ifeq(group_member(sk0(sk1(h,phi(f_left_zero))),f),true,multiply(h,phi(f_left_zero),phi(sk0(sk1(h,phi(f_left_zero))))),phi(f_left_zero)),
inference(step,[status(thm)],[t678,t258]) ).
cnf(t680,plain,
phi(f_left_zero) = ifeq(true,true,multiply(h,phi(f_left_zero),phi(sk0(sk1(h,phi(f_left_zero))))),phi(f_left_zero)),
inference(step,[status(thm)],[t679,t607]) ).
cnf(t681,plain,
phi(f_left_zero) = multiply(h,phi(f_left_zero),phi(sk0(sk1(h,phi(f_left_zero))))),
inference(step,[status(thm)],[t680,t258]) ).
cnf(c5,plain,
( phi(sk0(X0)) = X0
| ~ group_member(X0,h) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t25,plain,
ifeq(group_member(X1,h),true,phi(sk0(X1)),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t259,plain,
ifeq(group_member(X1,h),true,phi(sk0(X1)),X1) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t597,plain,
sk1(h,phi(f_left_zero)) = ifeq(true,true,phi(sk0(sk1(h,phi(f_left_zero)))),sk1(h,phi(f_left_zero))),
inference(cp,[status(thm)],[t259,t595]) ).
cnf(t673,plain,
sk1(h,phi(f_left_zero)) = phi(sk0(sk1(h,phi(f_left_zero)))),
inference(step,[status(thm)],[t597,t258]) ).
cnf(t620,plain,
phi(sk0(sk1(h,phi(f_left_zero)))) = sk1(h,phi(f_left_zero)),
inference(orient,[status(thm)],[t673]) ).
cnf(t682,plain,
phi(f_left_zero) = multiply(h,phi(f_left_zero),sk1(h,phi(f_left_zero))),
inference(step,[status(thm)],[t681,t620]) ).
cnf(t636,plain,
multiply(h,phi(f_left_zero),sk1(h,phi(f_left_zero))) = phi(f_left_zero),
inference(orient,[status(thm)],[t682]) ).
cnf(t638,plain,
true = ifeq(group_member(phi(f_left_zero),h),true,ifeq(phi(f_left_zero),phi(f_left_zero),left_zero(h,phi(f_left_zero)),true),true),
inference(cp,[status(thm)],[t555,t636]) ).
cnf(t683,plain,
true = ifeq(true,true,ifeq(phi(f_left_zero),phi(f_left_zero),left_zero(h,phi(f_left_zero)),true),true),
inference(step,[status(thm)],[t638,t505]) ).
cnf(t684,plain,
true = ifeq(phi(f_left_zero),phi(f_left_zero),left_zero(h,phi(f_left_zero)),true),
inference(step,[status(thm)],[t683,t258]) ).
cnf(t685,plain,
true = left_zero(h,phi(f_left_zero)),
inference(step,[status(thm)],[t684,t258]) ).
cnf(t686,plain,
true = false,
inference(step,[status(thm)],[t685,t588]) ).
cnf(t643,plain,
false = true,
inference(orient,[status(thm)],[t686]) ).
cnf(t687,plain,
left_zero(h,phi(f_left_zero)) = true,
inference(step,[status(thm)],[t588,t643]) ).
cnf(t644,plain,
left_zero(h,phi(f_left_zero)) = true,
inference(orient,[status(thm)],[t687]) ).
cnf(goal_0,negated_conjecture,
left_zero(h,phi(f_left_zero)) != true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t644]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.58 % Computer : n014.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Wed Sep 23 14:06:20 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 239.15/33.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 239.15/33.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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