%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 01:35:23 PM UTC 2026
% Result : Unsatisfiable 25.51s 5.28s
% Output : CNFRefutation 25.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn 103 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : product(X0,difference(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] : difference(X0,product(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1] : quotient(product(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
fof(f6,axiom,
! [X0,X1] : product(quotient(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
fof(f9,axiom,
! [X0] : i(X0) = difference(X0,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
fof(f10,axiom,
! [X0] : j(X0) = quotient(one,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
fof(f32,axiom,
! [X2,X0,X1] : product(a(X0,X1,X2),difference(X2,product(a(X2,X0,X1),X2))) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos29) ).
fof(f33,plain,
! [X2,X0,X1] : one = product(a(X0,X1,X2),difference(X2,product(a(X2,X0,X1),X2))),
inference(reorient_equations,[],[f32]) ).
fof(f34,axiom,
! [X2,X0,X1] : a(X0,i(X1),X2) = a(X0,j(X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos30) ).
fof(f35,axiom,
! [X2,X0,X1] : a(i(X0),X1,X2) = a(j(X0),X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos31) ).
fof(f36,axiom,
! [X2,X0,X1] : a(j(X0),X1,X2) = a(X1,X2,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos32) ).
fof(f37,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f49,plain,
! [X2,X0,X1] : a(X0,difference(X1,one),X2) = a(X0,quotient(one,X1),X2),
inference(definition_unfolding,[],[f34,f9,f10]) ).
fof(f50,plain,
! [X2,X0,X1] : a(difference(X0,one),X1,X2) = a(quotient(one,X0),X1,X2),
inference(definition_unfolding,[],[f35,f9,f10]) ).
fof(f51,plain,
! [X2,X0,X1] : a(X1,X2,X0) = a(quotient(one,X0),X1,X2),
inference(definition_unfolding,[],[f36,f10]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] : product(a(X0,X1,X2),difference(X2,product(a(X2,X0,X1),X2))) = one,
inference(cnf_transformation,[],[f33]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] : a(X0,difference(X1,one),X2) = a(X0,quotient(one,X1),X2),
inference(cnf_transformation,[],[f49]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] : a(difference(X0,one),X1,X2) = a(quotient(one,X0),X1,X2),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] : a(quotient(one,X0),X1,X2) = a(X1,X2,X0),
inference(cnf_transformation,[],[f51]) ).
tcf(c_110,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i,X2: $i] : a(difference(X0,one),X1,X2) = a(X1,X2,X0),
inference(light_normalisation,[status(thm)],[c_108,c_109]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i,X2: $i] : product(a(difference(X0,one),X1,X2),difference(X2,product(a(X2,quotient(one,X0),X1),X2))) = one,
inference(superposition,[status(thm)],[c_107,c_106]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] : product(a(X0,X1,X2),difference(X1,product(a(X1,quotient(one,X2),X0),X1))) = one,
inference(light_normalisation,[status(thm)],[c_323,c_196]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i,X2: $i] : product(a(X0,quotient(one,X1),X2),difference(difference(X1,one),product(a(difference(X1,one),quotient(one,X2),X0),difference(X1,one)))) = one,
inference(superposition,[status(thm)],[c_107,c_324]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i,X2: $i] : product(a(X0,quotient(one,X1),X2),difference(difference(X1,one),product(a(X0,X1,X2),difference(X1,one)))) = one,
inference(demodulation,[status(thm)],[c_327,c_109,c_196]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(a(X0,X1,X2),X0)) = difference(a(X1,X2,X0),one),
inference(superposition,[status(thm)],[c_106,c_85]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,one),product(a(X1,X0,X2),difference(X0,one))) = difference(a(X1,quotient(one,X0),X2),one),
inference(superposition,[status(thm)],[c_334,c_85]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] : quotient(X0,difference(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_84,c_86]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i] : difference(quotient(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_87,c_85]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i] : a(X0,quotient(one,quotient(one,X1)),X2) = a(X0,X1,X2),
inference(superposition,[status(thm)],[c_473,c_107]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(a(X1,quotient(one,X0),X2),X0)) = difference(a(X1,quotient(one,quotient(one,X0)),X2),one),
inference(superposition,[status(thm)],[c_473,c_387]) ).
tcf(c_1254,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(a(X1,quotient(one,X0),X2),X0)) = difference(a(X1,X0,X2),one),
inference(demodulation,[status(thm)],[c_727,c_519]) ).
tcf(c_1258,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(a(quotient(one,X0),X1,X2),X0)) = difference(a(quotient(one,X2),X0,X1),one),
inference(superposition,[status(thm)],[c_109,c_1254]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(a(X1,X2,X0),X0)) = difference(a(quotient(one,X2),X0,X1),one),
inference(light_normalisation,[status(thm)],[c_1258,c_109]) ).
tcf(c_1421,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(a(X1,X2,X0),X0)) = difference(a(X0,X1,X2),one),
inference(demodulation,[status(thm)],[c_1282,c_109]) ).
tcf(c_8203,plain,
! [X0: $i,X1: $i] : difference(a(X0,X0,X1),one) = difference(a(X1,X0,X0),one),
inference(superposition,[status(thm)],[c_380,c_1421]) ).
tcf(c_28372,plain,
! [X0: $i,X1: $i] : quotient(one,difference(a(X0,X1,X1),one)) = a(X1,X1,X0),
inference(superposition,[status(thm)],[c_8203,c_412]) ).
tcf(c_40378,plain,
! [X0: $i,X1: $i] : a(X0,X0,X1) = a(X1,X0,X0),
inference(demodulation,[status(thm)],[c_28372,c_412]) ).
tcf(c_40379,plain,
a(x1,x1,x0) != a(x1,x1,x0),
inference(demodulation,[status(thm)],[c_110,c_40378]) ).
tcf(c_40380,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_40379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 15:58:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running UEQ theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 25.51/5.28 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 25.51/5.28 % SZS status Started for theBenchmark.p
% 25.51/5.28 % SZS status Unsatisfiable for theBenchmark.p
% 25.51/5.28
% 25.51/5.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.51/5.28
% 25.51/5.28 % ------ iProver source info
% 25.51/5.28
% 25.51/5.28 % git: date: 2026-07-19 20:42:38 +0200
% 25.51/5.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.51/5.28 % git: non_committed_changes: false
% 25.51/5.28
% 25.51/5.28 % ------ Parsing...% successful
% 25.51/5.28
% 25.51/5.28
% 25.51/5.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.51/5.28
% 25.51/5.28 % ------ Preprocessing... sup_sim: 9 sf_s rm: 0 0s sf_e pe_s pe_e %
% 25.51/5.28
% 25.51/5.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 25.51/5.28
% 25.51/5.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 25.51/5.28 % ------ Proving...
% 25.51/5.28 % ------ Problem Properties
% 25.51/5.28
% 25.51/5.28 %
% 25.51/5.28 % clauses 29
% 25.51/5.28 % conjectures 1
% 25.51/5.28 % EPR 0
% 25.51/5.28 % Horn 29
% 25.51/5.28 % unary 29
% 25.51/5.28 % binary 0
% 25.51/5.28 % lits 29
% 25.51/5.28 % lits eq 29
% 25.51/5.28 % fd_pure 0
% 25.51/5.28 % fd_pseudo 0
% 25.51/5.28 % fd_cond 0
% 25.51/5.28 % fd_pseudo_cond 0
% 25.51/5.28 % AC symbols 0
% 25.51/5.28
% 25.51/5.28 % ------ Input Options Time Limit: Unbounded
% 25.51/5.28
% 25.51/5.28
% 25.51/5.28 % ------
% 25.51/5.28 % Current options:
% 25.51/5.28 % ------
% 25.51/5.28
% 25.51/5.28
% 25.51/5.28 %
% 25.51/5.28
% 25.51/5.28 % ------ Proving...
% 25.51/5.28 %
% 25.51/5.28
% 25.51/5.28 % SZS status Unsatisfiable for theBenchmark.p
% 25.51/5.28
% 25.51/5.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.51/5.28
% 25.51/5.28
%------------------------------------------------------------------------------