%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 02:38:06 PM UTC 2026
% Result : Unsatisfiable 4.13s 1.19s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% 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 : 8 ( 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; 0-4 aty)
% Number of variables : 103 ( 0 sgn 103 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X0] : sum(additive_identity,X0,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f4,axiom,
! [X0] : sum(X0,additive_identity,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f5,plain,
! [X0] : true = sum(X0,additive_identity,X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f7,plain,
! [X0,X1] : true = product(X0,X1,multiply(X0,X1)),
inference(reorient_equations,[],[f6]) ).
fof(f12,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f13,plain,
! [X0] : true = sum(X0,additive_inverse(X0),additive_identity),
inference(reorient_equations,[],[f12]) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f25,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true),
inference(reorient_equations,[],[f24]) ).
fof(f32,axiom,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f34,axiom,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X3,X2),true,X3,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
fof(f36,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
fof(f37,plain,
true != product(a,additive_identity,additive_identity),
inference(reorient_equations,[],[f36]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_73,plain,
! [X0: $i] : sum(additive_identity,X0,X0) = true,
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,plain,
! [X0: $i] : sum(X0,additive_identity,X0) = true,
inference(cnf_transformation,[],[f5]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity) = true,
inference(cnf_transformation,[],[f13]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
inference(cnf_transformation,[],[f25]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[],[f32]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X3,X2),true,X3,X1),X1) = X1,
inference(cnf_transformation,[],[f34]) ).
tcf(c_92,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
inference(cnf_transformation,[],[f37]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ifeq(product(X0,additive_identity,X1),true,ifeq(product(X0,additive_inverse(X2),X3),true,ifeq(product(X0,X2,X4),true,ifeq(true,true,sum(X4,X3,X1),true),true),true),true) = true,
inference(superposition,[status(thm)],[c_78,c_84]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ifeq(product(X0,additive_identity,X1),true,ifeq(product(X0,additive_inverse(X2),X3),true,ifeq(product(X0,X2,X4),true,sum(X4,X3,X1),true),true),true) = true,
inference(demodulation,[status(thm)],[c_256,c_72]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq(product(X0,additive_identity,X1),true,ifeq(product(X0,additive_inverse(X2),X3),true,ifeq(true,true,sum(multiply(X0,X2),X3,X1),true),true),true) = true,
inference(superposition,[status(thm)],[c_75,c_268]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq(product(X0,additive_identity,X1),true,ifeq(product(X0,additive_inverse(X2),X3),true,sum(multiply(X0,X2),X3,X1),true),true) = true,
inference(demodulation,[status(thm)],[c_309,c_72]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,ifeq(product(X0,additive_inverse(X1),X2),true,sum(multiply(X0,X1),X2,multiply(X0,additive_identity)),true),true) = true,
inference(superposition,[status(thm)],[c_75,c_343]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(product(X0,additive_inverse(X1),X2),true,sum(multiply(X0,X1),X2,multiply(X0,additive_identity)),true) = true,
inference(demodulation,[status(thm)],[c_344,c_72]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] : ifeq(true,true,sum(multiply(X0,X1),multiply(X0,additive_inverse(X1)),multiply(X0,additive_identity)),true) = true,
inference(superposition,[status(thm)],[c_75,c_356]) ).
tcf(c_711,plain,
! [X0: $i,X1: $i] : ifeq2(true,true,ifeq2(sum(additive_identity,X0,X1),true,X1,X0),X0) = X0,
inference(superposition,[status(thm)],[c_73,c_88]) ).
tcf(c_733,plain,
! [X0: $i,X1: $i] : ifeq2(sum(additive_identity,X0,X1),true,X1,X0) = X0,
inference(demodulation,[status(thm)],[c_711,c_71]) ).
tcf(c_737,plain,
ifeq2(true,true,additive_identity,additive_inverse(additive_identity)) = additive_inverse(additive_identity),
inference(superposition,[status(thm)],[c_78,c_733]) ).
tcf(c_801,plain,
additive_inverse(additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_737,c_71]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i] : ifeq2(true,true,ifeq2(sum(X0,X1,X0),true,X1,additive_identity),additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_74,c_90]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i] : ifeq2(sum(X0,X1,X0),true,X1,additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_1262,c_71]) ).
tcf(c_1909,plain,
! [X0: $i,X1: $i] : sum(multiply(X0,X1),multiply(X0,additive_inverse(X1)),multiply(X0,additive_identity)) = true,
inference(demodulation,[status(thm)],[c_357,c_72]) ).
tcf(c_1958,plain,
! [X0: $i] : ifeq2(true,true,multiply(X0,additive_inverse(additive_identity)),additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_1909,c_1298]) ).
tcf(c_1959,plain,
! [X0: $i] : ifeq2(true,true,multiply(X0,additive_identity),additive_identity) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1958,c_801]) ).
tcf(c_2032,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_1959,c_71]) ).
tcf(c_2114,plain,
! [X0: $i] : product(X0,additive_identity,additive_identity) = true,
inference(superposition,[status(thm)],[c_2032,c_75]) ).
tcf(c_2134,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_92,c_2114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 07:39:48 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running UEQ theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 4.13/1.19 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 4.13/1.19 % SZS status Started for theBenchmark.p
% 4.13/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/1.19
% 4.13/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.13/1.19
% 4.13/1.19 % ------ iProver source info
% 4.13/1.19
% 4.13/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 4.13/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.13/1.19 % git: non_committed_changes: false
% 4.13/1.19
% 4.13/1.19 % ------ Parsing...% successful
% 4.13/1.19
% 4.13/1.19
% 4.13/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.13/1.19
% 4.13/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.13/1.19
% 4.13/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.13/1.19
% 4.13/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.13/1.19 % ------ Proving...
% 4.13/1.19 % ------ Problem Properties
% 4.13/1.19
% 4.13/1.19 %
% 4.13/1.19 % clauses 22
% 4.13/1.19 % conjectures 1
% 4.13/1.19 % EPR 0
% 4.13/1.19 % Horn 22
% 4.13/1.19 % unary 22
% 4.13/1.19 % binary 0
% 4.13/1.19 % lits 22
% 4.13/1.19 % lits eq 22
% 4.13/1.19 % fd_pure 0
% 4.13/1.19 % fd_pseudo 0
% 4.13/1.19 % fd_cond 0
% 4.13/1.19 % fd_pseudo_cond 0
% 4.13/1.19 % AC symbols 0
% 4.13/1.19
% 4.13/1.19 % ------ Input Options Time Limit: Unbounded
% 4.13/1.19
% 4.13/1.19
% 4.13/1.19 % ------
% 4.13/1.19 % Current options:
% 4.13/1.19 % ------
% 4.13/1.19
% 4.13/1.19
% 4.13/1.19 %
% 4.13/1.19
% 4.13/1.19 % ------ Proving...
% 4.13/1.19 %
% 4.13/1.19
% 4.13/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/1.19
% 4.13/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.13/1.19
% 4.13/1.19
%------------------------------------------------------------------------------