%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO017-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 01:00:14 PM UTC 2026
% Result : Unsatisfiable 14.88s 21.91s
% Output : CNFRefutation 14.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 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 : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 122 ( 0 sgn 122 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f4,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f5,plain,
! [X0,X1] : true = product(X0,X1,multiply(X0,X1)),
inference(reorient_equations,[],[f4]) ).
fof(f10,axiom,
! [X0] : sum(additive_identity,X0,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f11,plain,
! [X0] : true = sum(additive_identity,X0,X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0] : sum(X0,additive_identity,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f13,plain,
! [X0] : true = sum(X0,additive_identity,X0),
inference(reorient_equations,[],[f12]) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X1,X5),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f25,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X1,X5),true),true),true),true),
inference(reorient_equations,[],[f24]) ).
fof(f26,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X1,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X5,X4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity5) ).
fof(f27,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X1,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X5,X4),true),true),true),true),
inference(reorient_equations,[],[f26]) ).
fof(f38,axiom,
! [X0] : product(inverse(X0),X0,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f39,plain,
! [X0] : true = product(inverse(X0),X0,additive_identity),
inference(reorient_equations,[],[f38]) ).
fof(f43,axiom,
! [X2,X3,X0,X1] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f44,axiom,
sum(x,y,z) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
fof(f45,plain,
true = sum(x,y,z),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
product(x,z,x) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
fof(f47,plain,
true != product(x,z,x),
inference(reorient_equations,[],[f46]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[],[f5]) ).
tcf(c_81,plain,
! [X0: $i] : sum(additive_identity,X0,X0) = true,
inference(cnf_transformation,[],[f11]) ).
tcf(c_82,plain,
! [X0: $i] : sum(X0,additive_identity,X0) = true,
inference(cnf_transformation,[],[f13]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X1,X5),true),true),true),true) = true,
inference(cnf_transformation,[],[f25]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : ifeq(product(X0,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X1,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X5,X4),true),true),true),true) = true,
inference(cnf_transformation,[],[f27]) ).
tcf(c_95,plain,
! [X0: $i] : product(inverse(X0),X0,additive_identity) = true,
inference(cnf_transformation,[],[f39]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[],[f43]) ).
tcf(c_99,plain,
sum(x,y,z) = true,
inference(cnf_transformation,[],[f45]) ).
tcf(c_100,negated_conjecture,
product(x,z,x) != true,
inference(cnf_transformation,[],[f47]) ).
tcf(c_44891,plain,
! [X0: $i,X1: $i] : ifeq2(product(inverse(X0),X0,X1),true,ifeq2(true,true,additive_identity,X1),X1) = X1,
inference(superposition,[status(thm)],[c_95,c_98]) ).
tcf(c_44897,plain,
! [X0: $i,X1: $i] : ifeq2(product(inverse(X0),X0,X1),true,additive_identity,X1) = X1,
inference(demodulation,[status(thm)],[c_44891,c_75]) ).
tcf(c_45310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,X3),true,ifeq(sum(X3,X1,X4),true,ifeq(true,true,product(X2,X0,X4),true),true),true),true) = true,
inference(superposition,[status(thm)],[c_82,c_88]) ).
tcf(c_45324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,X3),true,ifeq(sum(X3,X1,X4),true,product(X2,X0,X4),true),true),true) = true,
inference(demodulation,[status(thm)],[c_45310,c_76]) ).
tcf(c_45368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ifeq(product(additive_identity,X0,X1),true,ifeq(sum(X2,X1,X3),true,ifeq(sum(X2,X0,X4),true,ifeq(true,true,product(X2,X4,X3),true),true),true),true) = true,
inference(superposition,[status(thm)],[c_82,c_89]) ).
tcf(c_45382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ifeq(product(additive_identity,X0,X1),true,ifeq(sum(X2,X1,X3),true,ifeq(sum(X2,X0,X4),true,product(X2,X4,X3),true),true),true) = true,
inference(demodulation,[status(thm)],[c_45368,c_76]) ).
tcf(c_52780,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,additive_identity),true,ifeq(true,true,product(X2,X0,X1),true),true),true) = true,
inference(superposition,[status(thm)],[c_81,c_45324]) ).
tcf(c_52818,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,additive_identity),true,product(X2,X0,X1),true),true) = true,
inference(demodulation,[status(thm)],[c_52780,c_76]) ).
tcf(c_53359,plain,
! [X0: $i,X1: $i] : ifeq(product(additive_identity,X0,X1),true,ifeq(true,true,product(inverse(X0),X0,X1),true),true) = true,
inference(superposition,[status(thm)],[c_95,c_52818]) ).
tcf(c_53372,plain,
! [X0: $i,X1: $i] : ifeq(product(additive_identity,X0,X1),true,product(inverse(X0),X0,X1),true) = true,
inference(demodulation,[status(thm)],[c_53359,c_76]) ).
tcf(c_53614,plain,
! [X0: $i] : ifeq(true,true,product(inverse(X0),X0,multiply(additive_identity,X0)),true) = true,
inference(superposition,[status(thm)],[c_78,c_53372]) ).
tcf(c_53633,plain,
! [X0: $i] : product(inverse(X0),X0,multiply(additive_identity,X0)) = true,
inference(superposition,[status(thm)],[c_53614,c_76]) ).
tcf(c_53678,plain,
! [X0: $i] : ifeq2(true,true,additive_identity,multiply(additive_identity,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_53633,c_44897]) ).
tcf(c_53688,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_53678,c_75]) ).
tcf(c_53746,plain,
! [X0: $i] : product(additive_identity,X0,additive_identity) = true,
inference(superposition,[status(thm)],[c_53688,c_78]) ).
tcf(c_70131,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(product(additive_identity,X0,additive_identity),true,ifeq(true,true,ifeq(sum(X1,X0,X2),true,product(X1,X2,X1),true),true),true) = true,
inference(superposition,[status(thm)],[c_82,c_45382]) ).
tcf(c_70219,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(sum(X0,X1,X2),true,product(X0,X2,X0),true) = true,
inference(demodulation,[status(thm)],[c_70131,c_76,c_53746]) ).
tcf(c_74263,plain,
ifeq(true,true,product(x,z,x),true) = true,
inference(superposition,[status(thm)],[c_99,c_70219]) ).
tcf(c_74338,plain,
product(x,z,x) = true,
inference(superposition,[status(thm)],[c_76,c_74263]) ).
tcf(c_74340,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_74338,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO017-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.62 % CPULimit : 300
% 0.07/15.63 % WCLimit : 300
% 0.07/15.63 % DateTime : Fri Sep 25 06:33:29 UTC 2026
% 0.07/15.63 % CPUTime :
% 0.07/15.63 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/15.66 Running UEQ theorem proving
% 0.07/15.66 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/15.68
% 0.07/15.68 % ======== iProver multi-core TPTP/SMT =========
% 0.07/15.68
% 0.07/15.68 % Detected problem language: tptp
% 0.07/15.69 % Proving...
% 14.88/21.91 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 14.88/21.91 % SZS status Started for theBenchmark.p
% 14.88/21.91 % SZS status Unsatisfiable for theBenchmark.p
% 14.88/21.91
% 14.88/21.91 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.88/21.91
% 14.88/21.91 % ------ iProver source info
% 14.88/21.91
% 14.88/21.91 % git: date: 2026-07-19 20:42:38 +0200
% 14.88/21.91 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.88/21.91 % git: non_committed_changes: false
% 14.88/21.91
% 14.88/21.91 % ------ Parsing...% successful
% 14.88/21.91
% 14.88/21.91
% 14.88/21.91 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.88/21.91
% 14.88/21.91 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 14.88/21.91
% 14.88/21.91 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.88/21.91
% 14.88/21.91 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 14.88/21.91 % ------ Proving...
% 14.88/21.91 % ------ Problem Properties
% 14.88/21.91
% 14.88/21.91 %
% 14.88/21.91 % clauses 26
% 14.88/21.91 % conjectures 1
% 14.88/21.91 % EPR 0
% 14.88/21.91 % Horn 26
% 14.88/21.91 % unary 26
% 14.88/21.91 % binary 0
% 14.88/21.91 % lits 26
% 14.88/21.91 % lits eq 26
% 14.88/21.91 % fd_pure 0
% 14.88/21.91 % fd_pseudo 0
% 14.88/21.91 % fd_cond 0
% 14.88/21.91 % fd_pseudo_cond 0
% 14.88/21.91 % AC symbols 0
% 14.88/21.91
% 14.88/21.91 % ------ Input Options Time Limit: Unbounded
% 14.88/21.91
% 14.88/21.91
% 14.88/21.91 % ------
% 14.88/21.91 % Current options:
% 14.88/21.91 % ------
% 14.88/21.91
% 14.88/21.91
% 14.88/21.91 %
% 14.88/21.91
% 14.88/21.91 % ------ Proving...
% 14.88/21.91 %
% 14.88/21.91
% 14.88/21.91 % SZS status Unsatisfiable for theBenchmark.p
% 14.88/21.91
% 14.88/21.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.88/21.91
% 14.88/21.91
%------------------------------------------------------------------------------