%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Tue May 5 07:00:00 PM UTC 2026 % Result : Theorem 19.23s 6.52s % Output : Proof 23.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0. % 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.17/0.34 % Computer : n027.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue May 5 11:35:19 EDT 2026 % 0.17/0.35 % CPUTime : % 0.52/0.60 ____ _ % 0.52/0.60 ___ / __ \_____(_)___ ________ __________ % 0.52/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.60 % 0.52/0.60 A Theorem Prover for First-Order Logic % 0.52/0.60 (ePrincess v.1.0) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2015 % 0.52/0.60 (c) Peter Backeman, 2014-2015 % 0.52/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.60 Bug reports to peter@backeman.se % 0.52/0.60 % 0.52/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.42/0.96 Prover 0: Preprocessing ... % 2.14/1.21 Prover 0: Warning: ignoring some quantifiers % 2.14/1.23 Prover 0: Constructing countermodel ... % 16.54/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 16.54/5.98 Prover 1: Preprocessing ... % 17.12/6.07 Prover 1: Constructing countermodel ... % 17.62/6.14 Prover 1: gave up % 17.62/6.14 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 17.62/6.15 Prover 2: Preprocessing ... % 17.95/6.21 Prover 2: Warning: ignoring some quantifiers % 17.95/6.21 Prover 2: Constructing countermodel ... % 19.23/6.51 Prover 2: proved (378ms) % 19.23/6.52 Prover 0: stopped % 19.23/6.52 % 19.23/6.52 No countermodel exists, formula is valid % 19.23/6.52 % SZS status Theorem for theBenchmark % 19.23/6.52 % 19.23/6.52 Generating proof ... Warning: ignoring some quantifiers % 23.19/7.41 found it (size 60) % 23.19/7.41 % 23.19/7.41 % SZS output start Proof for theBenchmark % 23.19/7.41 Assumed formulas after preprocessing and simplification: % 23.19/7.41 | (0) ? [v0] : ? [v1] : ( ~ (pE = pB) & ~ (pE = pA) & ~ (pB = pA) & ~ (a = b) & linP(pE) = nil & linP(pB) = v1 & linP(pA) = v0 & cons(a, nil) = v0 & cons(b, nil) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (linP(v3) = v5) | ~ (linP(v2) = v4) | ~ (append(v4, v5) = v6) | ? [v7] : (linC(v7) = v6 & c2(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (append(v5, v2) = v6) | ~ (cons(v3, v4) = v5) | ? [v7] : (append(v4, v2) = v7 & cons(v3, v7) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (append(v4, v2) = v5) | ~ (cons(v3, v5) = v6) | ? [v7] : (append(v7, v2) = v6 & cons(v3, v4) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (append(v5, v4) = v3) | ~ (append(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (c2(v5, v4) = v3) | ~ (c2(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (cons(v5, v4) = v3) | ~ (cons(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (linC(v4) = v3) | ~ (linC(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (linC(v3) = v4) | ~ (linC(v2) = v4)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (linP(v4) = v3) | ~ (linP(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (proj2C(v4) = v3) | ~ (proj2C(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (proj1C(v4) = v3) | ~ (proj1C(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (bP(v4) = v3) | ~ (bP(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (proj1BP(v4) = v3) | ~ (proj1BP(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (aP(v4) = v3) | ~ (aP(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (proj1AP(v4) = v3) | ~ (proj1AP(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (tail(v4) = v3) | ~ (tail(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (head(v4) = v3) | ~ (head(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (c2(v2, v3) = v4) | proj2C(v4) = v3) & ! [v2] : ! [v3] : ! [v4] : ( ~ (c2(v2, v3) = v4) | proj1C(v4) = v2) & ! [v2] : ! [v3] : ! [v4] : ( ~ (c2(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (linC(v4) = v5 & linP(v3) = v7 & linP(v2) = v6 & append(v6, v7) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (bP(v3) = v4) | ~ (aP(v2) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v2, v3) = v4) | tail(v4) = v3) & ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v2, v3) = v4) | head(v4) = v2) & ! [v2] : ! [v3] : (v3 = v2 | ~ (append(nil, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (linP(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (linP(v4) = v5 & append(v3, v1) = v6 & append(v1, v6) = v5 & bP(v2) = v4)) & ! [v2] : ! [v3] : ( ~ (linP(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (linP(v4) = v5 & append(v3, v0) = v6 & append(v0, v6) = v5 & aP(v2) = v4)) & ! [v2] : ! [v3] : ( ~ (bP(v2) = v3) | proj1BP(v3) = v2) & ! [v2] : ! [v3] : ( ~ (bP(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (linP(v3) = v4 & linP(v2) = v5 & append(v5, v1) = v6 & append(v1, v6) = v4)) & ! [v2] : ! [v3] : ( ~ (aP(v2) = v3) | proj1AP(v3) = v2) & ! [v2] : ! [v3] : ( ~ (aP(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (linP(v3) = v4 & linP(v2) = v5 & append(v5, v0) = v6 & append(v0, v6) = v4)) & ! [v2] : ! [v3] : ~ (cons(v2, v3) = nil) & ! [v2] : ~ (bP(v2) = pE) & ! [v2] : ~ (bP(v2) = pB) & ! [v2] : ~ (bP(v2) = pA) & ! [v2] : ~ (aP(v2) = pE) & ! [v2] : ~ (aP(v2) = pB) & ! [v2] : ~ (aP(v2) = pA) & ? [v2] : ? [v3] : ? [v4] : append(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : c2(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : cons(v3, v2) = v4 & ? [v2] : ? [v3] : linC(v2) = v3 & ? [v2] : ? [v3] : linP(v2) = v3 & ? [v2] : ? [v3] : proj2C(v2) = v3 & ? [v2] : ? [v3] : proj1C(v2) = v3 & ? [v2] : ? [v3] : bP(v2) = v3 & ? [v2] : ? [v3] : proj1BP(v2) = v3 & ? [v2] : ? [v3] : aP(v2) = v3 & ? [v2] : ? [v3] : proj1AP(v2) = v3 & ? [v2] : ? [v3] : tail(v2) = v3 & ? [v2] : ? [v3] : head(v2) = v3) % 23.19/7.45 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 23.19/7.45 | (1) ~ (pE = pB) & ~ (pE = pA) & ~ (pB = pA) & ~ (a = b) & linP(pE) = nil & linP(pB) = all_0_0_0 & linP(pA) = all_0_1_1 & cons(a, nil) = all_0_1_1 & cons(b, nil) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (linP(v1) = v3) | ~ (linP(v0) = v2) | ~ (append(v2, v3) = v4) | ? [v5] : (linC(v5) = v4 & c2(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (append(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ? [v5] : (append(v2, v0) = v5 & cons(v1, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (append(v2, v0) = v3) | ~ (cons(v1, v3) = v4) | ? [v5] : (append(v5, v0) = v4 & cons(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (append(v3, v2) = v1) | ~ (append(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (c2(v3, v2) = v1) | ~ (c2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (linC(v2) = v1) | ~ (linC(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (linC(v1) = v2) | ~ (linC(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (linP(v2) = v1) | ~ (linP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj2C(v2) = v1) | ~ (proj2C(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj1C(v2) = v1) | ~ (proj1C(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bP(v2) = v1) | ~ (bP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj1BP(v2) = v1) | ~ (proj1BP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aP(v2) = v1) | ~ (aP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj1AP(v2) = v1) | ~ (proj1AP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tail(v2) = v1) | ~ (tail(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (c2(v0, v1) = v2) | proj2C(v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (c2(v0, v1) = v2) | proj1C(v2) = v0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (c2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (linC(v2) = v3 & linP(v1) = v5 & linP(v0) = v4 & append(v4, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (bP(v1) = v2) | ~ (aP(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | tail(v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | head(v2) = v0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (append(nil, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (linP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v2) = v3 & append(v1, all_0_0_0) = v4 & append(all_0_0_0, v4) = v3 & bP(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (linP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v2) = v3 & append(v1, all_0_1_1) = v4 & append(all_0_1_1, v4) = v3 & aP(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (bP(v0) = v1) | proj1BP(v1) = v0) & ! [v0] : ! [v1] : ( ~ (bP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v1) = v2 & linP(v0) = v3 & append(v3, all_0_0_0) = v4 & append(all_0_0_0, v4) = v2)) & ! [v0] : ! [v1] : ( ~ (aP(v0) = v1) | proj1AP(v1) = v0) & ! [v0] : ! [v1] : ( ~ (aP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v1) = v2 & linP(v0) = v3 & append(v3, all_0_1_1) = v4 & append(all_0_1_1, v4) = v2)) & ! [v0] : ! [v1] : ~ (cons(v0, v1) = nil) & ! [v0] : ~ (bP(v0) = pE) & ! [v0] : ~ (bP(v0) = pB) & ! [v0] : ~ (bP(v0) = pA) & ! [v0] : ~ (aP(v0) = pE) & ! [v0] : ~ (aP(v0) = pB) & ! [v0] : ~ (aP(v0) = pA) & ? [v0] : ? [v1] : ? [v2] : append(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : c2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : cons(v1, v0) = v2 & ? [v0] : ? [v1] : linC(v0) = v1 & ? [v0] : ? [v1] : linP(v0) = v1 & ? [v0] : ? [v1] : proj2C(v0) = v1 & ? [v0] : ? [v1] : proj1C(v0) = v1 & ? [v0] : ? [v1] : bP(v0) = v1 & ? [v0] : ? [v1] : proj1BP(v0) = v1 & ? [v0] : ? [v1] : aP(v0) = v1 & ? [v0] : ? [v1] : proj1AP(v0) = v1 & ? [v0] : ? [v1] : tail(v0) = v1 & ? [v0] : ? [v1] : head(v0) = v1 % 23.19/7.45 | % 23.19/7.45 | Applying alpha-rule on (1) yields: % 23.19/7.45 | (2) ? [v0] : ? [v1] : head(v0) = v1 % 23.19/7.46 | (3) ? [v0] : ? [v1] : proj2C(v0) = v1 % 23.19/7.46 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (linP(v2) = v1) | ~ (linP(v2) = v0)) % 23.19/7.46 | (5) ? [v0] : ? [v1] : linP(v0) = v1 % 23.19/7.46 | (6) ! [v0] : ! [v1] : ( ~ (bP(v0) = v1) | proj1BP(v1) = v0) % 23.19/7.46 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj1C(v2) = v1) | ~ (proj1C(v2) = v0)) % 23.19/7.46 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (c2(v0, v1) = v2) | proj2C(v2) = v1) % 23.19/7.46 | (9) linP(pA) = all_0_1_1 % 23.19/7.46 | (10) ! [v0] : ! [v1] : ( ~ (bP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v1) = v2 & linP(v0) = v3 & append(v3, all_0_0_0) = v4 & append(all_0_0_0, v4) = v2)) % 23.19/7.46 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | head(v2) = v0) % 23.19/7.46 | (12) cons(a, nil) = all_0_1_1 % 23.19/7.46 | (13) cons(b, nil) = all_0_0_0 % 23.19/7.46 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | tail(v2) = v1) % 23.19/7.46 | (15) linP(pE) = nil % 23.19/7.46 | (16) ? [v0] : ? [v1] : bP(v0) = v1 % 23.19/7.46 | (17) ! [v0] : ~ (bP(v0) = pE) % 23.19/7.46 | (18) ? [v0] : ? [v1] : proj1AP(v0) = v1 % 23.19/7.46 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (linC(v1) = v2) | ~ (linC(v0) = v2)) % 23.19/7.46 | (20) ! [v0] : ! [v1] : ( ~ (aP(v0) = v1) | proj1AP(v1) = v0) % 23.19/7.46 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 23.19/7.46 | (22) ? [v0] : ? [v1] : linC(v0) = v1 % 23.19/7.46 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (linP(v1) = v3) | ~ (linP(v0) = v2) | ~ (append(v2, v3) = v4) | ? [v5] : (linC(v5) = v4 & c2(v0, v1) = v5)) % 23.19/7.46 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (c2(v3, v2) = v1) | ~ (c2(v3, v2) = v0)) % 23.19/7.46 | (25) ? [v0] : ? [v1] : proj1C(v0) = v1 % 23.19/7.46 | (26) ? [v0] : ? [v1] : ? [v2] : append(v1, v0) = v2 % 23.19/7.46 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bP(v2) = v1) | ~ (bP(v2) = v0)) % 23.19/7.46 | (28) ~ (pE = pB) % 23.19/7.46 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj2C(v2) = v1) | ~ (proj2C(v2) = v0)) % 23.19/7.46 | (30) ! [v0] : ! [v1] : ( ~ (linP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v2) = v3 & append(v1, all_0_0_0) = v4 & append(all_0_0_0, v4) = v3 & bP(v0) = v2)) % 23.19/7.46 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aP(v2) = v1) | ~ (aP(v2) = v0)) % 23.19/7.46 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tail(v2) = v1) | ~ (tail(v2) = v0)) % 23.19/7.46 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj1BP(v2) = v1) | ~ (proj1BP(v2) = v0)) % 23.19/7.46 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (append(v2, v0) = v3) | ~ (cons(v1, v3) = v4) | ? [v5] : (append(v5, v0) = v4 & cons(v1, v2) = v5)) % 23.19/7.46 | (35) linP(pB) = all_0_0_0 % 23.19/7.46 | (36) ! [v0] : ~ (aP(v0) = pE) % 23.19/7.46 | (37) ! [v0] : ! [v1] : ~ (cons(v0, v1) = nil) % 23.19/7.46 | (38) ~ (a = b) % 23.19/7.46 | (39) ? [v0] : ? [v1] : proj1BP(v0) = v1 % 23.19/7.46 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (proj1AP(v2) = v1) | ~ (proj1AP(v2) = v0)) % 23.19/7.46 | (41) ! [v0] : ~ (aP(v0) = pB) % 23.19/7.46 | (42) ~ (pE = pA) % 23.19/7.46 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (append(nil, v0) = v1)) % 23.19/7.46 | (44) ? [v0] : ? [v1] : ? [v2] : cons(v1, v0) = v2 % 23.19/7.46 | (45) ~ (pB = pA) % 23.19/7.46 | (46) ! [v0] : ~ (aP(v0) = pA) % 23.19/7.46 | (47) ? [v0] : ? [v1] : ? [v2] : c2(v1, v0) = v2 % 23.19/7.46 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (c2(v0, v1) = v2) | proj1C(v2) = v0) % 23.19/7.46 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (bP(v1) = v2) | ~ (aP(v0) = v2)) % 23.19/7.46 | (50) ! [v0] : ~ (bP(v0) = pB) % 23.19/7.46 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) % 23.19/7.46 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (append(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ? [v5] : (append(v2, v0) = v5 & cons(v1, v5) = v4)) % 23.19/7.46 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (linC(v2) = v1) | ~ (linC(v2) = v0)) % 23.19/7.46 | (54) ? [v0] : ? [v1] : aP(v0) = v1 % 23.19/7.46 | (55) ! [v0] : ! [v1] : ( ~ (linP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v2) = v3 & append(v1, all_0_1_1) = v4 & append(all_0_1_1, v4) = v3 & aP(v0) = v2)) % 23.19/7.46 | (56) ! [v0] : ! [v1] : ( ~ (aP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (linP(v1) = v2 & linP(v0) = v3 & append(v3, all_0_1_1) = v4 & append(all_0_1_1, v4) = v2)) % 23.19/7.47 | (57) ? [v0] : ? [v1] : tail(v0) = v1 % 23.19/7.47 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (append(v3, v2) = v1) | ~ (append(v3, v2) = v0)) % 23.19/7.47 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (c2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (linC(v2) = v3 & linP(v1) = v5 & linP(v0) = v4 & append(v4, v5) = v3)) % 23.19/7.47 | (60) ! [v0] : ~ (bP(v0) = pA) % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (30) with nil, pE and discharging atoms linP(pE) = nil, yields: % 23.19/7.47 | (61) ? [v0] : ? [v1] : ? [v2] : (linP(v0) = v1 & append(all_0_0_0, v2) = v1 & append(nil, all_0_0_0) = v2 & bP(pE) = v0) % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (55) with nil, pE and discharging atoms linP(pE) = nil, yields: % 23.19/7.47 | (62) ? [v0] : ? [v1] : ? [v2] : (linP(v0) = v1 & append(all_0_1_1, v2) = v1 & append(nil, all_0_1_1) = v2 & aP(pE) = v0) % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (30) with all_0_0_0, pB and discharging atoms linP(pB) = all_0_0_0, yields: % 23.19/7.47 | (63) ? [v0] : ? [v1] : ? [v2] : (linP(v0) = v1 & append(all_0_0_0, v2) = v1 & append(all_0_0_0, all_0_0_0) = v2 & bP(pB) = v0) % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (55) with all_0_1_1, pA and discharging atoms linP(pA) = all_0_1_1, yields: % 23.19/7.47 | (64) ? [v0] : ? [v1] : ? [v2] : (linP(v0) = v1 & append(all_0_1_1, v2) = v1 & append(all_0_1_1, all_0_1_1) = v2 & aP(pA) = v0) % 23.19/7.47 | % 23.19/7.47 | Instantiating (62) with all_37_0_34, all_37_1_35, all_37_2_36 yields: % 23.19/7.47 | (65) linP(all_37_2_36) = all_37_1_35 & append(all_0_1_1, all_37_0_34) = all_37_1_35 & append(nil, all_0_1_1) = all_37_0_34 & aP(pE) = all_37_2_36 % 23.19/7.47 | % 23.19/7.47 | Applying alpha-rule on (65) yields: % 23.19/7.47 | (66) linP(all_37_2_36) = all_37_1_35 % 23.19/7.47 | (67) append(all_0_1_1, all_37_0_34) = all_37_1_35 % 23.19/7.47 | (68) append(nil, all_0_1_1) = all_37_0_34 % 23.19/7.47 | (69) aP(pE) = all_37_2_36 % 23.19/7.47 | % 23.19/7.47 | Instantiating (61) with all_39_0_37, all_39_1_38, all_39_2_39 yields: % 23.19/7.47 | (70) linP(all_39_2_39) = all_39_1_38 & append(all_0_0_0, all_39_0_37) = all_39_1_38 & append(nil, all_0_0_0) = all_39_0_37 & bP(pE) = all_39_2_39 % 23.19/7.47 | % 23.19/7.47 | Applying alpha-rule on (70) yields: % 23.19/7.47 | (71) linP(all_39_2_39) = all_39_1_38 % 23.19/7.47 | (72) append(all_0_0_0, all_39_0_37) = all_39_1_38 % 23.19/7.47 | (73) append(nil, all_0_0_0) = all_39_0_37 % 23.19/7.47 | (74) bP(pE) = all_39_2_39 % 23.19/7.47 | % 23.19/7.47 | Instantiating (63) with all_41_0_40, all_41_1_41, all_41_2_42 yields: % 23.19/7.47 | (75) linP(all_41_2_42) = all_41_1_41 & append(all_0_0_0, all_41_0_40) = all_41_1_41 & append(all_0_0_0, all_0_0_0) = all_41_0_40 & bP(pB) = all_41_2_42 % 23.19/7.47 | % 23.19/7.47 | Applying alpha-rule on (75) yields: % 23.19/7.47 | (76) linP(all_41_2_42) = all_41_1_41 % 23.19/7.47 | (77) append(all_0_0_0, all_41_0_40) = all_41_1_41 % 23.19/7.47 | (78) append(all_0_0_0, all_0_0_0) = all_41_0_40 % 23.19/7.47 | (79) bP(pB) = all_41_2_42 % 23.19/7.47 | % 23.19/7.47 | Instantiating (64) with all_43_0_43, all_43_1_44, all_43_2_45 yields: % 23.19/7.47 | (80) linP(all_43_2_45) = all_43_1_44 & append(all_0_1_1, all_43_0_43) = all_43_1_44 & append(all_0_1_1, all_0_1_1) = all_43_0_43 & aP(pA) = all_43_2_45 % 23.19/7.47 | % 23.19/7.47 | Applying alpha-rule on (80) yields: % 23.19/7.47 | (81) linP(all_43_2_45) = all_43_1_44 % 23.19/7.47 | (82) append(all_0_1_1, all_43_0_43) = all_43_1_44 % 23.19/7.47 | (83) append(all_0_1_1, all_0_1_1) = all_43_0_43 % 23.19/7.47 | (84) aP(pA) = all_43_2_45 % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (43) with all_39_0_37, all_0_0_0 and discharging atoms append(nil, all_0_0_0) = all_39_0_37, yields: % 23.19/7.47 | (85) all_39_0_37 = all_0_0_0 % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (43) with all_37_0_34, all_0_1_1 and discharging atoms append(nil, all_0_1_1) = all_37_0_34, yields: % 23.19/7.47 | (86) all_37_0_34 = all_0_1_1 % 23.19/7.47 | % 23.19/7.47 | From (85) and (72) follows: % 23.19/7.47 | (87) append(all_0_0_0, all_0_0_0) = all_39_1_38 % 23.19/7.47 | % 23.19/7.47 | From (86) and (67) follows: % 23.19/7.47 | (88) append(all_0_1_1, all_0_1_1) = all_37_1_35 % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (58) with all_0_0_0, all_0_0_0, all_39_1_38, all_41_0_40 and discharging atoms append(all_0_0_0, all_0_0_0) = all_41_0_40, append(all_0_0_0, all_0_0_0) = all_39_1_38, yields: % 23.19/7.47 | (89) all_41_0_40 = all_39_1_38 % 23.19/7.47 | % 23.19/7.47 | Instantiating formula (58) with all_0_1_1, all_0_1_1, all_37_1_35, all_43_0_43 and discharging atoms append(all_0_1_1, all_0_1_1) = all_43_0_43, append(all_0_1_1, all_0_1_1) = all_37_1_35, yields: % 23.19/7.47 | (90) all_43_0_43 = all_37_1_35 % 23.19/7.47 | % 23.19/7.47 | From (89) and (77) follows: % 23.19/7.47 | (91) append(all_0_0_0, all_39_1_38) = all_41_1_41 % 23.19/7.47 | % 23.19/7.47 | From (89) and (78) follows: % 23.19/7.47 | (87) append(all_0_0_0, all_0_0_0) = all_39_1_38 % 23.19/7.47 | % 23.19/7.47 | From (90) and (82) follows: % 23.19/7.48 | (93) append(all_0_1_1, all_37_1_35) = all_43_1_44 % 23.19/7.48 | % 23.19/7.48 | From (90) and (83) follows: % 23.19/7.48 | (88) append(all_0_1_1, all_0_1_1) = all_37_1_35 % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (52) with all_41_1_41, all_0_0_0, nil, b, all_39_1_38 and discharging atoms append(all_0_0_0, all_39_1_38) = all_41_1_41, cons(b, nil) = all_0_0_0, yields: % 23.19/7.48 | (95) ? [v0] : (append(nil, all_39_1_38) = v0 & cons(b, v0) = all_41_1_41) % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (23) with all_39_1_38, all_0_0_0, all_0_0_0, pB, pB and discharging atoms linP(pB) = all_0_0_0, append(all_0_0_0, all_0_0_0) = all_39_1_38, yields: % 23.19/7.48 | (96) ? [v0] : (linC(v0) = all_39_1_38 & c2(pB, pB) = v0) % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (52) with all_43_1_44, all_0_1_1, nil, a, all_37_1_35 and discharging atoms append(all_0_1_1, all_37_1_35) = all_43_1_44, cons(a, nil) = all_0_1_1, yields: % 23.19/7.48 | (97) ? [v0] : (append(nil, all_37_1_35) = v0 & cons(a, v0) = all_43_1_44) % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (23) with all_37_1_35, all_0_1_1, all_0_1_1, pA, pA and discharging atoms linP(pA) = all_0_1_1, append(all_0_1_1, all_0_1_1) = all_37_1_35, yields: % 23.19/7.48 | (98) ? [v0] : (linC(v0) = all_37_1_35 & c2(pA, pA) = v0) % 23.19/7.48 | % 23.19/7.48 | Instantiating (98) with all_65_0_51 yields: % 23.19/7.48 | (99) linC(all_65_0_51) = all_37_1_35 & c2(pA, pA) = all_65_0_51 % 23.19/7.48 | % 23.19/7.48 | Applying alpha-rule on (99) yields: % 23.19/7.48 | (100) linC(all_65_0_51) = all_37_1_35 % 23.19/7.48 | (101) c2(pA, pA) = all_65_0_51 % 23.19/7.48 | % 23.19/7.48 | Instantiating (97) with all_75_0_56 yields: % 23.19/7.48 | (102) append(nil, all_37_1_35) = all_75_0_56 & cons(a, all_75_0_56) = all_43_1_44 % 23.19/7.48 | % 23.19/7.48 | Applying alpha-rule on (102) yields: % 23.19/7.48 | (103) append(nil, all_37_1_35) = all_75_0_56 % 23.19/7.48 | (104) cons(a, all_75_0_56) = all_43_1_44 % 23.19/7.48 | % 23.19/7.48 | Instantiating (96) with all_77_0_57 yields: % 23.19/7.48 | (105) linC(all_77_0_57) = all_39_1_38 & c2(pB, pB) = all_77_0_57 % 23.19/7.48 | % 23.19/7.48 | Applying alpha-rule on (105) yields: % 23.19/7.48 | (106) linC(all_77_0_57) = all_39_1_38 % 23.19/7.48 | (107) c2(pB, pB) = all_77_0_57 % 23.19/7.48 | % 23.19/7.48 | Instantiating (95) with all_87_0_62 yields: % 23.19/7.48 | (108) append(nil, all_39_1_38) = all_87_0_62 & cons(b, all_87_0_62) = all_41_1_41 % 23.19/7.48 | % 23.19/7.48 | Applying alpha-rule on (108) yields: % 23.19/7.48 | (109) append(nil, all_39_1_38) = all_87_0_62 % 23.19/7.48 | (110) cons(b, all_87_0_62) = all_41_1_41 % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (43) with all_87_0_62, all_39_1_38 and discharging atoms append(nil, all_39_1_38) = all_87_0_62, yields: % 23.19/7.48 | (111) all_87_0_62 = all_39_1_38 % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (43) with all_75_0_56, all_37_1_35 and discharging atoms append(nil, all_37_1_35) = all_75_0_56, yields: % 23.19/7.48 | (112) all_75_0_56 = all_37_1_35 % 23.19/7.48 | % 23.19/7.48 | From (111) and (109) follows: % 23.19/7.48 | (113) append(nil, all_39_1_38) = all_39_1_38 % 23.19/7.48 | % 23.19/7.48 | From (112) and (103) follows: % 23.19/7.48 | (114) append(nil, all_37_1_35) = all_37_1_35 % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (23) with all_39_1_38, all_39_1_38, nil, all_39_2_39, pE and discharging atoms linP(all_39_2_39) = all_39_1_38, linP(pE) = nil, append(nil, all_39_1_38) = all_39_1_38, yields: % 23.19/7.48 | (115) ? [v0] : (linC(v0) = all_39_1_38 & c2(pE, all_39_2_39) = v0) % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (23) with all_37_1_35, all_37_1_35, nil, all_37_2_36, pE and discharging atoms linP(all_37_2_36) = all_37_1_35, linP(pE) = nil, append(nil, all_37_1_35) = all_37_1_35, yields: % 23.19/7.48 | (116) ? [v0] : (linC(v0) = all_37_1_35 & c2(pE, all_37_2_36) = v0) % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (48) with all_77_0_57, pB, pB and discharging atoms c2(pB, pB) = all_77_0_57, yields: % 23.19/7.48 | (117) proj1C(all_77_0_57) = pB % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (48) with all_65_0_51, pA, pA and discharging atoms c2(pA, pA) = all_65_0_51, yields: % 23.19/7.48 | (118) proj1C(all_65_0_51) = pA % 23.19/7.48 | % 23.19/7.48 | Instantiating (116) with all_193_0_142 yields: % 23.19/7.48 | (119) linC(all_193_0_142) = all_37_1_35 & c2(pE, all_37_2_36) = all_193_0_142 % 23.19/7.48 | % 23.19/7.48 | Applying alpha-rule on (119) yields: % 23.19/7.48 | (120) linC(all_193_0_142) = all_37_1_35 % 23.19/7.48 | (121) c2(pE, all_37_2_36) = all_193_0_142 % 23.19/7.48 | % 23.19/7.48 | Instantiating (115) with all_195_0_143 yields: % 23.19/7.48 | (122) linC(all_195_0_143) = all_39_1_38 & c2(pE, all_39_2_39) = all_195_0_143 % 23.19/7.48 | % 23.19/7.48 | Applying alpha-rule on (122) yields: % 23.19/7.48 | (123) linC(all_195_0_143) = all_39_1_38 % 23.19/7.48 | (124) c2(pE, all_39_2_39) = all_195_0_143 % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (19) with all_39_1_38, all_195_0_143, all_77_0_57 and discharging atoms linC(all_195_0_143) = all_39_1_38, linC(all_77_0_57) = all_39_1_38, yields: % 23.19/7.48 | (125) all_195_0_143 = all_77_0_57 % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (19) with all_37_1_35, all_193_0_142, all_65_0_51 and discharging atoms linC(all_193_0_142) = all_37_1_35, linC(all_65_0_51) = all_37_1_35, yields: % 23.19/7.48 | (126) all_193_0_142 = all_65_0_51 % 23.19/7.48 | % 23.19/7.48 | From (125) and (124) follows: % 23.19/7.48 | (127) c2(pE, all_39_2_39) = all_77_0_57 % 23.19/7.48 | % 23.19/7.48 | From (126) and (121) follows: % 23.19/7.48 | (128) c2(pE, all_37_2_36) = all_65_0_51 % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (48) with all_77_0_57, all_39_2_39, pE and discharging atoms c2(pE, all_39_2_39) = all_77_0_57, yields: % 23.19/7.48 | (129) proj1C(all_77_0_57) = pE % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (48) with all_65_0_51, all_37_2_36, pE and discharging atoms c2(pE, all_37_2_36) = all_65_0_51, yields: % 23.19/7.48 | (130) proj1C(all_65_0_51) = pE % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (7) with all_77_0_57, pE, pB and discharging atoms proj1C(all_77_0_57) = pE, proj1C(all_77_0_57) = pB, yields: % 23.19/7.48 | (131) pE = pB % 23.19/7.48 | % 23.19/7.48 | Instantiating formula (7) with all_65_0_51, pE, pA and discharging atoms proj1C(all_65_0_51) = pE, proj1C(all_65_0_51) = pA, yields: % 23.19/7.48 | (132) pE = pA % 23.19/7.48 | % 23.19/7.49 | Combining equations (131,132) yields a new equation: % 23.19/7.49 | (133) pB = pA % 23.19/7.49 | % 23.19/7.49 | Simplifying 133 yields: % 23.19/7.49 | (134) pB = pA % 23.19/7.49 | % 23.19/7.49 | Equations (134) can reduce 45 to: % 23.19/7.49 | (135) $false % 23.19/7.49 | % 23.19/7.49 |-The branch is then unsatisfiable % 23.19/7.49 % SZS output end Proof for theBenchmark % 23.19/7.49 % 23.19/7.49 6876ms %------------------------------------------------------------------------------